Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The extreme values of $4 cos invisible function application open parentheses x to the power of 2 end exponent close parentheses cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction plus x to the power of 2 end exponent close parentheses cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction minus x to the power of 2 end exponent close parentheses$ over $R$ , are

-1, 1
-2, 2
-3, 3
-4, 4

The correct answer is: -1, 1

Let $f open parentheses x close parentheses equals 4 cos invisible function application left parenthesis x to the power of 2 end exponent right parenthesis cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction plus x to the power of 2 end exponent close parentheses cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction minus x to the power of 2 end exponent close parentheses$
$equals 2 cos invisible function application open parentheses x to the power of 2 end exponent close parentheses open square brackets cos invisible function application open parentheses fraction numerator 2 pi over denominator 3 end fraction close parentheses plus cos invisible function application open parentheses 2 x to the power of 2 end exponent close parentheses close square brackets$

$open square brackets because blank 2 cos invisible function application A cos invisible function application B equals cos invisible function application open parentheses A plus B close parentheses plus cos invisible function application open parentheses A minus B close parentheses close square brackets$

$equals 2 cos invisible function application left parenthesis x to the power of 2 end exponent right parenthesis open square brackets negative fraction numerator 1 over denominator 2 end fraction plus cos invisible function application left parenthesis 2 x to the power of 2 end exponent right parenthesis close square brackets$

$equals negative cos invisible function application open parentheses x to the power of 2 end exponent close parentheses plus 2 cos invisible function application open parentheses x to the power of 2 end exponent close parentheses cos invisible function application open parentheses 2 x to the power of 2 end exponent close parentheses$

$equals negative cos invisible function application open parentheses x to the power of 2 end exponent close parentheses plus cos invisible function application open parentheses 3 x to the power of 2 end exponent close parentheses plus cos invisible function application open parentheses x to the power of 2 end exponent close parentheses$

$rightwards double arrow blank f open parentheses x close parentheses equals cos invisible function application left parenthesis 3 x to the power of 2 end exponent right parenthesis$ ...(i)

$rightwards double arrow blank f to the power of ´ end exponent open parentheses x close parentheses equals negative open square brackets sin invisible function application open parentheses 3 x to the power of 2 end exponent close parentheses close square brackets left parenthesis 6 x right parenthesis$

For extremum, put $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

$rightwards double arrow blank minus sin invisible function application open parentheses 3 x to the power of 2 end exponent close parentheses open parentheses 6 x close parentheses equals 0$

$rightwards double arrow blank x equals 0 comma blank square root of pi$

Put $x equals 0 comma blank square root of pi$ in Eq. (i), we get

$f open parentheses 0 close parentheses equals cos invisible function application open parentheses 0 close parentheses equals 1$

And $f open parentheses pi close parentheses equals cos invisible function application left parenthesis 3 pi right parenthesis equals negative 1$

Related Questions to study

If the function $f colon R rightwards arrow R$ be defined by $f open parentheses x close parentheses equals tan invisible function application x minus x$ , then $f left parenthesis x right parenthesis$

If the function $f colon R rightwards arrow R$ be defined by $f open parentheses x close parentheses equals tan invisible function application x minus x$ , then $f left parenthesis x right parenthesis$

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ , at $x equals 1$ is

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ , at $x equals 1$ is

The function $f open parentheses x close parentheses equals log subscript e end subscript invisible function application open parentheses x to the power of 3 end exponent plus square root of x to the power of 6 end exponent plus 1 end root close parentheses$ is of the following types:

The function $f open parentheses x close parentheses equals log subscript e end subscript invisible function application open parentheses x to the power of 3 end exponent plus square root of x to the power of 6 end exponent plus 1 end root close parentheses$ is of the following types:

parallel

For the curve $y equals x blank e to the power of x end exponent$ , the point

For the curve $y equals x blank e to the power of x end exponent$ , the point

If the semi-vertical angle of a cone is $45 degree$ , then the rate of change of volume of the cone is

If the semi-vertical angle of a cone is $45 degree$ , then the rate of change of volume of the cone is

Let $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 end subscript close parentheses equals g open parentheses x subscript 0 end subscript close parentheses comma f to the power of ´ end exponent open parentheses x close parentheses greater than g ´ left parenthesis x right parenthesis$ for $x greater than x subscript 0 end subscript comma$ then

Let $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 end subscript close parentheses equals g open parentheses x subscript 0 end subscript close parentheses comma f to the power of ´ end exponent open parentheses x close parentheses greater than g ´ left parenthesis x right parenthesis$ for $x greater than x subscript 0 end subscript comma$ then

parallel

The equation of the normal line to the curve $y equals x log subscript e end subscript invisible function application x$ parallel to $2 x minus 2 y plus 3 equals 0$ is

The equation of the normal line to the curve $y equals x log subscript e end subscript invisible function application x$ parallel to $2 x minus 2 y plus 3 equals 0$ is

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ which is equal to

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ which is equal to

The length of subtangent to the curve $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$ at the point $left parenthesis negative a comma blank a right parenthesis$ is

The length of subtangent to the curve $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$ at the point $left parenthesis negative a comma blank a right parenthesis$ is

parallel

A ray of light is incident along vector $fraction numerator 1 over denominator square root of 2 end fraction i with not stretchy hat on top minus fraction numerator 1 over denominator square root of 2 end fraction j with not stretchy hat on top plus k with not stretchy hat on top$ on plane mirror placed in XY-plane normal on incidence point is along Z-axis

A ray of light is incident along vector $fraction numerator 1 over denominator square root of 2 end fraction i with not stretchy hat on top minus fraction numerator 1 over denominator square root of 2 end fraction j with not stretchy hat on top plus k with not stretchy hat on top$ on plane mirror placed in XY-plane normal on incidence point is along Z-axis

$text If end text a equals 3 i with not stretchy hat on top plus 4 j with not stretchy hat on top text and end text b equals 4 i with not stretchy hat on top minus 3 j with not stretchy hat on top comma text then end text$

$text If end text a equals 3 i with not stretchy hat on top plus 4 j with not stretchy hat on top text and end text b equals 4 i with not stretchy hat on top minus 3 j with not stretchy hat on top comma text then end text$

If unit vector $a equals a subscript 1 i with not stretchy hat on top plus a subscript 2 j with not stretchy hat on top plus a subscript 3 k with not stretchy hat on top$ . The possible values of a₁ a₂ and a₃ are

If unit vector $a equals a subscript 1 i with not stretchy hat on top plus a subscript 2 j with not stretchy hat on top plus a subscript 3 k with not stretchy hat on top$ . The possible values of a₁ a₂ and a₃ are

parallel

Current from $A blank a n d blank B$ in the straight wire is decreasing. The direction of induced current in the loop, is

Current from $A blank a n d blank B$ in the straight wire is decreasing. The direction of induced current in the loop, is

Physics-General

According to Lenz’s law of electromagnetic induction

According to Lenz’s law of electromagnetic induction

Physics-General

Two circular coils $A$ and $B$ are facing each other as shown in figure. When the current $i$ through $A$ is altered

Two circular coils $A$ and $B$ are facing each other as shown in figure. When the current $i$ through $A$ is altered

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.