Applications of Derivative - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

The radius of a circle is increasing uniformly at the rate of $3 cm / s$. Find the rate at which the area of the circle is increasing when the radius is 10 cm .

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Q 112 Marks Questions2 Marks

Find the maximum and minimum value of function $f(x)=\sin 2 x+5$.

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Q 122 Marks Questions2 Marks

Find the interval where function $f(x)=x^3-3 x$ is decreasing.

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Q 132 Marks Questions2 Marks

What is the maximum value of $a \sin x+b \cos x$ ?

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Q 142 Marks Questions2 Marks

For function $y=f(x)$ if $\frac{d y}{d x}=6(x-2)(x-3)$ then find the value of $x$ for the maximum value of $y$.

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Q 153 Marks Question3 Marks

Find the maximum value of $\sin \theta+\cos \theta$.

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Q 163 Marks Question3 Marks

A particle is moving in straight line such that on time $t$ distance ( $S$ ) from a fixed point is proportional to $n$ power of time. If at time $t$ its velocity $( V )$ and a acceleration then prove that :$
V^2=\frac{n a S}{(n-1)}
$

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Q 173 Marks Question3 Marks

Find the interval for which function $f(x)=x^3-$ $3 x^2-24 x+5$ is increasing.

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Q 183 Marks Question3 Marks

In interval $[ 1 , 5]$ Find the absolute maximum and absolute minimum values of given function $f(x)=x^2-4 x+8$.

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Q 193 Marks Question3 Marks

Radius of a sphere measure $9 \ cm$ in which error is $0.02 \ cm .$ Find the approximate error in calculation of volume.

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Q 205 Marks Questions5 Marks

Find the maximum and minimum value of this function.
$f(x)=\sec x+\log \cos ^2 x, 0 < x < 2 \pi $

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Q 215 Marks Questions5 Marks

Prove that function $\sin ^2 x(1+\cos x)$, at $\cos x =\frac{1}{3}$ is maximum.

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Q 225 Marks Questions5 Marks

In interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$, Find the difference in maximum value and minimum value of function $f(x)=\sin 2 x-x$.

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Q 23Fill In The Blanks[1 Marks ]1 Mark

The rate of change of the area of a circle with respect to its radius $r$ at $r=3 cm$ is ________ .

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Q 24Fill In The Blanks[1 Marks ]1 Mark

Those value of $x$ at which function $f(x)=\tan x-x$ is increasing _________ .

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Q 25Fill In The Blanks[1 Marks ]1 Mark

The maximum value of function $f(x)=\sin x+\cos x$ is _________ .

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Q 26Fill In The Blanks[1 Marks ]1 Mark

If in any circle radius is increasing at the rate of 0.5 $cm / sec$ then rate of increasing circumference is ________ .

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Q 27Fill In The Blanks[1 Marks ]1 Mark

Maximum value of $f(x)=x e^{-x}$ is _________ .

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Q 28Answer the question [ 4 mark question ]4 Marks

Surface area of a spherical bubble is increasing at the rate of $2 cm^2 / sec$. At what rate volume of bubble increasing when radius of bubble is $6 m$ ?

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Q 29Answer the question [ 4 mark question ]4 Marks

Find the maximum and minimum value of following function. $2 x^3-15 x^2+36 x+10$

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Applications of Derivative question types

Applications of Derivative questions

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Applications of Derivative MATHS - Applications of Derivative

Applications of Derivative question types

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