List of top Mathematics Questions on Application of derivatives

The slope of the tangent to the curve $y = x^{2 - x$ at the point where $x = 2$ is:

A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is

The function $f(x ) = xe^{1-x}$ is

The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

A circular sector of perimeter $60$ metre with maximum area is to be constructed. The radius of the circular arc in metre must be

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

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

If $f (x) = xe^{x(1-x)}$ , then f (x) is

Let $f(x) = (1 + b^2)x^2 + 2bx + 1$ and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

For all $x\,\in\,(0,1)$

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

A man of $2\,m$ height walks at a uniform speed of $6 \,km/h$ away from a lamp post of $6 \,m$ height. The rate at which the length of his shadow increases is

If $ \theta $ is semi vertical angle of a cone of maximum volume and given slant height, then $ tan\theta $ is equal to

Find the equation of normal to the curve$$y=(1+x{)}^y+{\sin }^{-1}({\sin }^{2}x)\text{at}x=0$$

Find the equation of normal to the curve$$y=(1+x)y+{\sin }^{-1}({\sin }^{2}x)\text{ at }x=0$$

The derivative of $se{c}^{-1} \left(\frac{1}{2x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ is:

Find the height of the right circular cone of maximum volume, which is inscribed in a sphere of radius 12cm.

Find the points on the curve \( y = 2x^3 - 3x^2 - 12x + 15 \) where rate of change of dependent variable with respect to the independent variable vanishes. What do we call these type of points?

The volume of spherical balloon is increasing at the rate of 25 c.c./s. Find the rate of change of its surface area at the instant when its radius is 5cm.

Radius of a circle is increasing at the rate of \( 2 \text{ m/s} \). Rate of change of its circumference is:

If the volume in $cm^3$ and surface area in $cm^2$ of a sphere are numerically equal. Then the radius of the sphere (in cm) is: