Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: TS EAMCET 2018 (04-May Shift-1)

A particle moves in a straight line such that its displacement $S$ (in $\mathrm{mts}$) at a time $t$ (in $\sec$) is given by $S\left(t\right)=t^3-4t^2+7t.$ The instantaneous velocity $v$ at $t=4$ is

The volume of a spherical balloon is increasing at the rate of $2{ \mathrm{cm}}^3/\sec .$ When its radius is $4 \mathrm{cm},$ the rate of change of its surface area (in $\mathrm{cm}{}^2/\sec$) is

The equation of the tangent to the curve $x{y}^5+2x^{2}y-x^3+y+1=0$ at $x=0$ is

If the tangent to the curve $xy+ax+by=0$ at $\left(1, 1\right)$ makes an angle $\tan {}^{-1}2$ with $x$-axis, then $\frac{a+b}{ab}=$

If the two curves $x=y^2$ and $xy=k$ cut each other at right angles, then a possible value of $k$ is

Let $R^{*}=R-\left\{(2k-1)\frac{\pi }{2}/k\in \mathrm{I}\right\}.$ The function $f : R^{*}\to R$ is defined as $f\left(x\right)=\tan x-x,$ then $f\left(x\right)$ is

The Rolle's theorem is not applicable to$f\left(x\right)=\left\{\begin{array}{cl}x,& 0\le x\le 1\\ 2-x,& 1\le x\le 2\end{array}\right.$ on $[0, 2]$ because

If a cubic function $f\left(x\right)=a{x}^3+b{x}^2-\frac{18}{5}x+\frac{19}{10}$ has maximum value $10$ at $x=-3$ and has minimum value $\frac{-5}{2}$ at $x=2,$ then $f\left(1\right)=$