List of top Mathematics Questions on Application of derivatives

The slope of the normal to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

The volume V and depth x of water in a vessl are connected by the relation $V = 5x - \frac{x^2}{6}$ and the volume of water is increasing , at the rate of $5 \, cm^3/sec$, when x = 2 cm. The rate at which the depth of water is increasing, is

The value of $c$ in Rolle's theorem for the function $f(x) = x^3 - 3x$ in the interval $\left[0, \sqrt{3}\right]$ is

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is

Let $F(x) = x^3 + ax^2 + bx + 5 sin^2\, x$ be an increasing function in the set of real number $R$. Then a and b satisfy the condition.

Let $f(x) = \cos x \sin 2x$, then

Let f and g be functions from the interval $[0, \infty)$ to the interval $[0, \infty)$,f being an increasing and g being a decreasing function. If f{g(0)} = 0 then

If $y = 3x^2 + 2$ and if x changes from 10 to 10.1, then the approximate change in y will be?

If $y = \frac{ax - b}{\left(x-1\right)\left(x-4\right)}$ has a turning point $P(2, -1)$, then find the value of $a$ and $b$ respectively.

If the radius of a spherical balloon increases by 0.2%. Find the percentage increase in its volume

If the normal to the curve $y^2 = 5x - 1$, at the point (1,- 2) is of the form ax - 5y + b = 0, then a and b are:

If the length of three sides of a trapezium other than base are equal to $10 \,cm$, then find the area of trapezium when it is maximum.

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4,$ then

If the curves $x^2 = 9A (9 - y)$ and $x^2 = A(y + 1)$ intersect orthogonally, then the value of A is

If tangent to the curve $y^2 = x^3$ at its point $(m^2, m^3)$ is also normal to the curve at $(M^2, M^3)$, then what is the value of mM ?

For the parabola $y^2 = 4ax, $ then ratio of the subtangent to the abscissa is

Find the points of local maxima and local minima respectively for the function $f\left(x\right) = sin\,2x-x$, where $-\frac{\pi}{2} \le x \le\frac{\pi }{2}$

Find the maximum profit that a company can make, if the profit function is given by $P(x) = 41 + 24x - 18x^2$.

Find the maximum value of $f(x) = sin(sinx)$ for all $x \in R$

Find the area of the largest isosceles triangle having perimeter $18$ metres.

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2\%$.

Find all the points of local maxima and local minima of the function $f(x) = (x - 1)^3 (x + 1)^2$

At ........... point on the parabola $x^2 = 4y$. the rate of increase of the x-coordinate is the same as the rate of the increasing y-coordinate.

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. The cost of the material will be least when depth of the tank is

An open box with a square base is to be made out of a given quantity of a cardboard of area $c^2$ square units. The maximum volume of the box is (in cubic units)