Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: Exercise 1

If atmosphere pressure at a height of $h$ units is given by the function $P\left(h\right)=h{e}^{-h}$ then pressure is maximum at the height of

If $f\left(x\right)=x{\left(1-x\right)}^3$ then which of following is true?

The cost function at American Gadget is $C\left(x\right)=x^3-6x^2+15x$ ($x$ is thousands of units and $x>0$). The production level at which average cost is minima is

Let $x$ be a number which exceeds it square by the greatest possible quantity. Then $x$ is equal to

The point $\left(0, 3\right)$ is nearest to the curve $x^2=2y$ at

If $x\in \left[-1, 1\right]$ then the minimum value of $f\left(x\right)=x^2+x+1$ is

The maximum value of $\cos \left[\cos \left(\sin x\right)\right]$ is

If $f\left(x\right)=\frac{p^2-1}{p^2+1}{x}^3-3x+\log 2$ is a decreasing function of $x$ in $R$ then the set of possible values of $p$ (independent of $x$) is