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Maths-

General

Easy

Question

The function $f open parentheses x close parentheses equals x to the power of 2 end exponent e to the power of negative x end exponent$ increases in the interval

(0, 2)
(2, 3)
(3, 4)
(4, 5)

The correct answer is: (0, 2)

Given, $f open parentheses x close parentheses equals x to the power of 2 end exponent e to the power of negative x end exponent$
$rightwards double arrow f to the power of ´ end exponent open parentheses x close parentheses equals 2 x e to the power of negative x end exponent minus x to the power of 2 end exponent e to the power of negative x end exponent$

For $f left parenthesis x right parenthesis$ To be increasing, $f to the power of ´ end exponent left parenthesis x right parenthesis greater than 0$

$rightwards double arrow 2 x e to the power of negative x end exponent minus x to the power of 2 end exponent e to the power of negative x end exponent greater than 0$

$rightwards double arrow e to the power of negative x end exponent left parenthesis 2 minus x right parenthesis greater than 0$

$rightwards double arrow x element of left parenthesis 02 right parenthesis$

Related Questions to study

The equation of tangent to the curve $y equals b e to the power of negative x divided by a end exponent$ at the point where it crosses $blank y minus$ axis, is

The equation of tangent to the curve $y equals b e to the power of negative x divided by a end exponent$ at the point where it crosses $blank y minus$ axis, is

At what point on the curve $x to the power of 3 end exponent minus 8 a to the power of 2 end exponent y equals 0$ , the slope of the normal is $negative fraction numerator 2 over denominator 3 end fraction$ ?

At what point on the curve $x to the power of 3 end exponent minus 8 a to the power of 2 end exponent y equals 0$ , the slope of the normal is $negative fraction numerator 2 over denominator 3 end fraction$ ?

If $f left parenthesis x right parenthesis$ is a function given by $f open parentheses x close parentheses equals open vertical bar table row cell sin invisible function application x end cell cell sin invisible function application a end cell cell sin invisible function application b end cell row cell cos invisible function application x end cell cell cos invisible function application a end cell cell cos invisible function application b end cell row cell tan invisible function application x end cell cell tan invisible function application a end cell cell tan invisible function application b end cell end table close vertical bar comma w h e r e blank 0 less than a less than b less than fraction numerator pi over denominator 2 end fraction$
Then the equation $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

If $f left parenthesis x right parenthesis$ is a function given by $f open parentheses x close parentheses equals open vertical bar table row cell sin invisible function application x end cell cell sin invisible function application a end cell cell sin invisible function application b end cell row cell cos invisible function application x end cell cell cos invisible function application a end cell cell cos invisible function application b end cell row cell tan invisible function application x end cell cell tan invisible function application a end cell cell tan invisible function application b end cell end table close vertical bar comma w h e r e blank 0 less than a less than b less than fraction numerator pi over denominator 2 end fraction$
Then the equation $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

parallel

A stone thrown upwards, has equation of motion $s equals 490 t minus 49 t to the power of 2 end exponent.$ Then, the maximum height reached by it ,is

A stone thrown upwards, has equation of motion $s equals 490 t minus 49 t to the power of 2 end exponent.$ Then, the maximum height reached by it ,is

If $theta$ is the angle between the curves $x y equals 2$ and $x to the power of 2 end exponent plus 4 y equals 0$ , then $tan invisible function application theta$ is equal to

If $theta$ is the angle between the curves $x y equals 2$ and $x to the power of 2 end exponent plus 4 y equals 0$ , then $tan invisible function application theta$ is equal to

Vector sum of two forces of 10 N and 6 N cannot be

Vector sum of two forces of 10 N and 6 N cannot be

parallel

For the resultant of two vectors to be maximum, what must be angle between them

For the resultant of two vectors to be maximum, what must be angle between them

The vector sum of the forces of 10 N and 6 N can be

The vector sum of the forces of 10 N and 6 N can be

$text Given: end text straight A with rightwards arrow on top equals 2 straight i with not stretchy hat on top plus 3 straight j with not stretchy hat on top text and end text straight B with rightwards arrow on top equals 5 straight i with not stretchy hat on top minus 6 straight j with not stretchy hat on top. text The magnitude of end text straight A with rightwards arrow on top plus straight B with rightwards arrow on top text is end text$

$text Given: end text straight A with rightwards arrow on top equals 2 straight i with not stretchy hat on top plus 3 straight j with not stretchy hat on top text and end text straight B with rightwards arrow on top equals 5 straight i with not stretchy hat on top minus 6 straight j with not stretchy hat on top. text The magnitude of end text straight A with rightwards arrow on top plus straight B with rightwards arrow on top text is end text$

parallel

The sum, difference and cross product of two vectors $straight A with rightwards arrow on top text and end text straight B with rightwards arrow on top$ are mutually perpendicular if

The sum, difference and cross product of two vectors $straight A with rightwards arrow on top text and end text straight B with rightwards arrow on top$ are mutually perpendicular if

What is the unit vector along $straight i with not stretchy hat on top plus straight j with not stretchy hat on top$ ?

What is the unit vector along $straight i with not stretchy hat on top plus straight j with not stretchy hat on top$ ?

In [0, 1] Lagranges Mean value theorem is NOT applicable to

In [0, 1] Lagranges Mean value theorem is NOT applicable to

parallel

The equation of the normal to the curve $y equals e to the power of negative 2 vertical line x vertical line end exponent$ at the point where the curve cuts the line $x equals 1 divided by 2$ , is

The equation of the normal to the curve $y equals e to the power of negative 2 vertical line x vertical line end exponent$ at the point where the curve cuts the line $x equals 1 divided by 2$ , is

The point in the interval $left square bracket 0 comma blank 2 pi right square bracket$ , where $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ has maximum slope is

The point in the interval $left square bracket 0 comma blank 2 pi right square bracket$ , where $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ has maximum slope 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 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

parallel

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