List of top Mathematics Questions on Application of derivatives asked in AP EAPCET

If the local maximum 'M' and local minimum 'm' of the function $f(x)=x-\frac{x^{2}}{2}-xe^{2-x}$ exist at $x=\alpha$ and $x=\beta$ respectively, then $2\alpha m+\beta M=$

If the length of the tangent at a point on the parabola $y^{2}=4ax$ is $4a\sqrt{5}$, then the length of the sub-normal at that point is

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be such that $f(2+x)=f(2-x)\,\,\forall x\in\mathbb{R}$. If $f(x)$ is twice differentiable such that $f^{\prime}(1)=0$, then which one of the following is true?

If \(f(x)=ax^{3}+bx^{2}+cx+1\) attains an extreme value \(2\) at \(x=1\) and another extreme value at \(x=\frac{2}{3}\), then \(2b+3c\) is equal to

If a cylindrical tank of radius 3 m is filled with water at the rate of \(\frac{3}{2} \, m^3/sec \), then the rate of change of its water level in (m/sec) is:

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at

The surface area of a cube is 150 sq. cm. If it is increased by 0.025 sq. cm, then the approximate increase in its volume (in c.c.) is:

The length of the tangent drawn at the point \(P(1, 3\sqrt{3})\) on the curve is \(\frac{x^2}{3} + \frac{y^2}{27} = 4\):

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

A balloon, which always remains spherical, has a variable radius. The rate at which its volume is increasing with respect to its radius $r$ when $r = 5$ cm is:

If the displacement of a particle at time $t$ ($0 < t < \pi$) is given by $s = 3 \sin 2t - 6 \cos t$, then the acceleration for the values of $t$ at which its velocity is zero is:

If the normal drawn to the curve \(y^4=16x^3\) at the point of intersection of this curve and the line \(y=2\) meets the \(X\)- and \(Y\)-axes at \(A\) and \(B\) respectively, then \(OA+3OB=\)

If the vertical angle of a cone is \(60^\circ\) and the rate of change of its total surface area is \(2\sqrt{3}\,\text{cm}^2/\text{sec}\), then the rate of change of its volume (in \(\text{cm}^3/\text{sec}\)) when its radius is \(5\) cm is:

The closest point on the parabola \[ y=x^2+7x+2 \] to the straight line \[ y=3x-2 \] is

The surface area of a sphere is \(49\pi\) sq.cm. If it is increased by \(0.016\) sq.cm., then the approximate increase in its volume (in c.c.) is:

The cubic equation \[ 2x^3-3x^2+6x+2=0 \]

Approximate value of \( \sqrt[3]{345} \), when it is calculated with the application of derivatives, is

The length of the normal drawn to the curve \( 2x^{3}+2y^{3}=9xy \) at the point (2, 1) is

If a sector of maximum area is made with a wire of length 40 cm, then the area (in sq cms) of that sector is

If the rate of increase in the surface area of a cube is 6 sq. cm./sec., then the rate of increase in its volume (in c. c./sec), when the length of its edge is 12 cm, is

The slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is:

The minimum value of \[ \left(1+\frac{1}{\sin^n\alpha}\right) \left(1+\frac{1}{\cos^n\alpha}\right) \] is

The sum of the intercepts made by a tangent drawn to the curve \((x/a)^n + (y/b)^n = 2\) at \((a,b)\) on the coordinate axes is

Maximum area of the rectangle inscribed in a circle of radius 10 cm is

If an open cylinder of given surface area has maximum volume, then its radius is