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Maths-

General

Easy

Question

Let $f open parentheses x close parentheses equals not stretchy integral e to the power of x end exponent open parentheses x minus 1 close parentheses left parenthesis x minus 2 right parenthesis d x$ . Then, $f$ decreases in the interval

$(- \infty, - 2)$
$(- 2, - 1)$
$(1, 2)$
$(2, \infty)$

The correct answer is: $left parenthesis 1 comma blank 2 right parenthesis$

Given that, $f open parentheses x close parentheses equals not stretchy integral e to the power of x end exponent open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses d x$
On differentiating w.r.t. $x$ , we get

$f to the power of ´ ´ end exponent open parentheses x close parentheses equals e to the power of x end exponent open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses$

Since, $f left parenthesis x right parenthesis$ is decreasing

$therefore blank f to the power of ´ ´ end exponent open parentheses x close parentheses less than 0 blank rightwards double arrow blank e to the power of x end exponent open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses less than 0$

$rightwards double arrow open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses less than 0 blank rightwards double arrow blank 1 less than x less than 2$

Related Questions to study

Consider the following statements $S$ and $R$ :
$S$ : Both $sin invisible function application x$ and $cos invisible function application x$ are decreasing function in $open parentheses fraction numerator pi over denominator 2 end fraction comma pi close parentheses$

$R$ : If a differentiating function decreases in $open parentheses a comma blank b close parentheses$ then its derivative also decreases in $open parentheses a comma blank b close parentheses$

Which of the following is true?

Consider the following statements $S$ and $R$ :
$S$ : Both $sin invisible function application x$ and $cos invisible function application x$ are decreasing function in $open parentheses fraction numerator pi over denominator 2 end fraction comma pi close parentheses$

$R$ : If a differentiating function decreases in $open parentheses a comma blank b close parentheses$ then its derivative also decreases in $open parentheses a comma blank b close parentheses$

Which of the following is true?

Which of the following functions is not decreasing on $left parenthesis 0 comma blank pi divided by 2 right parenthesis$ ?

Which of the following functions is not decreasing on $left parenthesis 0 comma blank pi divided by 2 right parenthesis$ ?

Coordinates of a point on the curve $y equals x log invisible function application x$ at which the normal is parallel to the line $2 x minus 2 y equals 3$ , are

Coordinates of a point on the curve $y equals x log invisible function application x$ at which the normal is parallel to the line $2 x minus 2 y equals 3$ , are

parallel

The sum of two numbers is 20. If the product of the square of one number and cube of the other is maximum, then the numbers are

The sum of two numbers is 20. If the product of the square of one number and cube of the other is maximum, then the numbers are

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If the velocity $upsilon$ of a particle moving along a straight line and its distance $s$ from a fixed point on the line are related by $upsilon to the power of 2 end exponent equals a to the power of 2 end exponent plus s to the power of 2 end exponent comma$ then its acceleration equals

If the velocity $upsilon$ of a particle moving along a straight line and its distance $s$ from a fixed point on the line are related by $upsilon to the power of 2 end exponent equals a to the power of 2 end exponent plus s to the power of 2 end exponent comma$ then its acceleration equals

parallel

The angle between the tangents to the curve $y to the power of 2 end exponent equals 2 a x$ at the point where $x equals fraction numerator a over denominator 2 end fraction$ , is

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$f left parenthesis x right parenthesis$ satisfies the conditions of Rolle’s theorem in [1, 2] and $f left parenthesis x right parenthesis$ is continuous in

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The maximum value of $x y$ when $x plus 2 y equals 8$ is

The maximum value of $x y$ when $x plus 2 y equals 8$ is

parallel

A vector perpendicular to $i with not stretchy hat on top plus j with not stretchy hat on top plus k with not stretchy hat on top$ is

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A man goes in for an examination in which there are four papers with a maximum of 'm' marks for each paper then the number of ways of getting 2m marks is

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The number of ways in which 12 students can be distributed among three sections is -

The number of ways in which 12 students can be distributed among three sections is -

parallel

The number of ways in which 19 different objects can be divided into two groups of 13 and 6 is -

The number of ways in which 19 different objects can be divided into two groups of 13 and 6 is -

In how many ways can 2n people be divided into n couples -

In how many ways can 2n people be divided into n couples -

A long solenoid has 500 turns. When a current of 2 ampere is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4 cross times 10 to the power of negative 3 end exponent W b$ . The self-inductance of the solenoid is

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Physics-General

parallel

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