Application of Derivatives · Mathematics · TS EAMCET

If $4+3 x-7 x^2$ attains its maximum value $M$ at $x=\alpha$ and $5 x^2-2 x+1$ attains its minimum value $m$ at $x=\beta$, then $\frac{28(M-a)}{5(m+\b...

If $x=\cos 2 t+\log (\tan t)$ and $y=2 t+\cot 2 t$, then $\frac{d y}{d x}=$

The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is

If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2$, then $\tan \theta=$

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured in to the cone at the rate of $\frac{1}{\sqrt{3}} \mathrm{~m}^3 ...

A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi-vertical angle of the cone is

If $f(x)=k x^3-3 x^2-12 x+8$ is strictly decreasing for all $x \in R$, then

The radius of a sphere is 7 cm . If an error of 0.08 sq cm is made in measuring it, then the approximate error (in cubic cm ) found in its volume is

The curve $y=x^3-2 x^2+3 x-4$ intersects the horizontal line $y=-2$ at the point $P(h, k)$. If the tangent drawn to this curve at $P$ meets the $X$-ax...

If $f(x)=(2 x-1)(3 x+2)(4 x-3)$ is a real valued function defined on $\left[\frac{1}{2}, \frac{3}{4}\right]$, then the value(s) of $c$ as defined in t...

If the interval in which the real valued function $f(x)=\log \left(\frac{1+x}{1-x}\right)-2 x-\frac{x^3}{1-x^2}$ is decreasing in $(a, b)$, where $|b-...

If the slope of the tangent drawn at any point $(x, y)$ on the curve $y=f(x)$ is $\left(6 x^2+10 x-9\right)$ and $f(2)=0$, then $f(-2)=$