Application of Derivatives PYQs - Last 10 Years

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Practice 116 AP EAPCET Mathematics questions from Application of Derivatives. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Application of Derivatives Questions

Showing 50 of 116 filtered questions.

1Application Of Derivatives

The point which lies on the tangent drawn to the curve $x^4 e^y+2 \sqrt{y+1}=3$ at the point $(1,0)$ is

2Application Of Derivatives

If $f(x)=x^x$, then the interval in which $f(x)$ decrease is

3Application Of Derivatives

If the Rolle's theorem is applicable for the function $f(x)$ defined by $f(x)=x^3+P x-12$ on $[0,1]$ then the value of $C$ of the Rolle's theorem is

4Application Of Derivatives

The distance ( s ) travelled by a particle in time $t$ is given by $S=4 t^2+2 t+3$. The velocity of the particle, when $t=3 \mathrm{sec}$ is

5Application Of Derivatives

If $a^2 x^4+b^2 y^4=c^6$, then maximum value of $x y$ is equal to

6Application Of Derivatives

If the percentage error in the radius of circle is 3 , then the percentage error in its area is

7Application Of Derivatives

If $x$ is real and $\alpha, \beta$ are maximum and minimum values of $\frac{x^2-x+1}{x^2+x+1}$ respectively, then $\alpha+\beta=$

8Application Of Derivatives

The equation of the tangent to the curve $y=x^3-2 x+7$ at the point $(1,6)$ is

9Application Of Derivatives

The value of $c$ such that the straight line joining the points $(0,3)$ and $(5,-2)$ is tangent to the curve $y=\frac{c}{x+1}$ is

10Application Of Derivatives

The angle between the curves $y^2=2 x$ and $x^2+y^2=8$ is

11Application Of Derivatives

If the function $f(x)=\sqrt{x^2-4}$ satisfies the Lagrange's mean value theorem on $[2,4]$, then the value of $C$ is

12Application Of Derivatives

If $x, y$ are two positive integers such that $x+y=20$ and the maximum value of $x^3 y$ is $k$ at $x=\alpha$ and $y=\beta$, then $\frac{k}{\alpha^2 \beta^2}=$

13Application Of Derivatives

If $T=2 \pi \sqrt{\frac{L}{g}}, \mathrm{~g}$ is a constant and the relative error in $T$ is $k$ times to the percentage error in $l$, then $\frac{1}{K}=$

14Application Of Derivatives

A' value of $C$ according to the Lagrange's mean value theorem for $f(x)=(x-1)(x-2)(x-3)$ in $[0,4]$ is

15Application Of Derivatives

Equation of a tagent line of the parabola $y^2=8 x$, which passes through the point $(1,3)$ is

16Application Of Derivatives

$p_1$ and $p_2$ are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ respectively. If $k_1 p_1^2+k_2 p_2^2=a^2$, then $k_1+k_2=$

17Application Of Derivatives

The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2 y$ is

18Application Of Derivatives

The length of the subnormal at any point on the curve $y=\left(\frac{x}{2024}\right)^k$ is constant, if the value of $k$ is

19Application Of Derivatives

For all $x \in[0,2024]$ assume that $f(x)$ is differentiable, $f(0)=-2$ and $f^{\prime}(x) \geq 5$. Then, the least possible value of $f(2024)$ is

20Application Of Derivatives

If the equation of tangent at $(2,3)$ on $y^2=a x^3+b$ is $y=4 x-5$, then the value of $a^2+b^2=$

21Application Of Derivatives

If $y=\left(1+\alpha+\alpha^2+\ldots\right) e^{\eta x}$, where $\alpha$ and $n$ are constants, then the relative error in $y$ is

22Application Of Derivatives

If Rolle's theorem is applicable for the function $f(x)=x(x+3) e^{-x / 2}$ on $[3,0]$, then the value of $c$ is

23Application Of Derivatives

The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing in its entire domain is

24Application Of Derivatives

A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the rate d 6 units per second. When the point is at $(2,-1)$, the rate of change of $x$-coordinate of the point is

25Application Of Derivatives

The number of points on the curve $y=2 t^2+3 t-5$ and $x=t^3-4 t^2-3 t$ such that the normals drawn at them on the curve are parallel to $X$-axis is

26Application Of Derivatives

If the tangent drawn to the curve $y=x^3-a x^2+x+1$ at each point $x \in R$, is inclined at an acute angle with the positive direction of $X$-axis, then the set of all possible values of ' $a$ ' is

27Application Of Derivatives

If $f(x)$ is a differentiable function, $f^{\prime}(x) \geq 5 \forall x \in[2,6]$, $f(2)=4$ and $f(3)=15$, then a possible value of $f(6)$

28Application Of Derivatives

If $f(x)=\sqrt{x+\sin x}$, then all the points of the set $\left\{(x, f(x)) / f^{\prime}(x)=0\right\}$ lie on

29Application Of Derivatives

Let $f(x)$ be a differentiable function, $A(0, \alpha)$ and $B(8, \beta)$ be two points on the curve $y=f(x)$. Given $f(0)=2$ and $f^{\prime}(4)=\frac{-3}{4}$. If the chord $A B$ of the curve is parallel to the tangent drawn at the point $(...

30Application Of Derivatives

If $A=\left\{9 x \geq x^2+20\right\}$ and $f: A \rightarrow R$ is defined by $f(x)=2 x^3-15 x^2+36 x-48$, then the maximum value of $f(x)$ is

31Application Of Derivatives

If the angle between the curves $y=e^{2(1+x)-4}$ and $x^2 y=1$ at the point $(1,1)$ is $\theta$, then $|\sin \theta|+|\cos \theta|=$

32Application Of Derivatives

If $(2, a)$ and $(b, 19)$ are two stationary points of the curve $y=2 x^3-15 x^2+36 x+c$, then $a+b+c=$

33Application Of Derivatives

If the points of contact of the tangents drawn from $(0,0)$ to the curve $y=x^2+3 x+4$ are $(\alpha, \beta)$ and $(\gamma, \delta)$, then $\beta+\delta=$

34Application Of Derivatives

The point on the curve \(y=x^2+4 x+3\) which is closest to the line \(y=3 x+2\) is

35Application Of Derivatives

If \(a, b>0\), then minimum value of \(y=\frac{b^2}{a-x}+\frac{a^2}{x}, 0< x< a\) is

36Application Of Derivatives

The line joining the points \((0,3)\) and \((5,-2)\) is a tangent to the curve \(y=\frac{c}{x+1}\), then \(c=\)

37Application Of Derivatives

If the normal drawn at a point \(P\) on the curve \(3 y=6 x-5 x^3\) passes through \((0,0)\), then the positive integral value of the abscissa of the point \(P\) is

38Application Of Derivatives

If \(3 f(\cos x)+2 f(\sin x)=5 x\), then \(f^{\prime}(\cos x)+f^{\prime}(\sin x)=\)

39Application Of Derivatives

The maximum value of \(f(x)=\frac{x}{1+4 x+x^2}\) is

40Application Of Derivatives

The minimum value of \(f(x)=x+\frac{4}{x+2}\) is

41Application Of Derivatives

If \(x^3-2 x^2 y^2+5 x+y-5=0\), then at \((\mathrm{l}, \mathrm{l}), y^{\prime \prime}(\mathrm{l})=\)

42Application Of Derivatives

The condition that \(f(x)=a x^3+b x^2+c x+d\) has no extreme value is

43Application Of Derivatives

If the curves \(y=x^3-3 x^2-8 x-4\) and \(y=3 x^2+7 x+4\) touch each other at a point \(P\), then the equation of common tangent at \(P\) is

44Application Of Derivatives

At any point \((x, y)\) on a curve if the length of the subnormal is \((x-1)\) and the curve passes through \((1,2)\), then the curve is a conic. A vertex of the curve is

45Application Of Derivatives

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

46Application Of Derivatives

Condition that 2 curves \(y^2=4 a x, x y=c^2\) cut orthogonally is

47Application Of Derivatives

If the straight line \(x \cos \alpha+y \sin \alpha=p\) touches the curve \(\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2\) at the point \((a, b)\) on it and \(\frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}\), then \(k=\)

48Application Of Derivatives

The number of those tangents to the curve \(y^2-2 x^3-4 y+8=0\) which pass through the point \((1,2)\) is

49Application Of Derivatives

Two particles \(P\) and \(Q\) located at the points \(P\left(t, t^3-16 t-3\right), Q\left(t+1, t^3-6 t-6\right)\) are moving in a plane, the minimum distance between the points in their motion is

50Application Of Derivatives

The diameter and altitude of a right circular
cone, at a certain instant, were found to be
10 cm and 20 cm respectively. If its diameter
is increasing at a rate of 2 cm/s, then at what
rate must its altitude change, in order to keep
its vol...