Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: KCET (UG) 2018

If the side of a cube is increased by $5\%$, then the surface area of a cube is increased by

Approximate change in volume $v$ of a cube of side $x$ metres caused by increasing the size by $3\%$ is

If the parabola $y=\alpha x^2-6x+\beta$ passes through the point $\left(0, 2\right)$ and has its tangent at $x=\frac{3}{2}$ parallel to $x$ axis, then

The function $f\left(x\right)=x^2-2x$ is strictly decreasing in the interval

The maximum value of ${\left(1/x\right)}^x$ is

$f\left(x\right)=x^x$ has stationary point at

The maximum area of a rectangle inscribed in the circle ${\left(x+1\right)}^2+{\left(y-3\right)}^2=64$ is

The maximum slope of the curve $y=-x^3+3x^2+2x-27$ is