Amit M Agarwal Solutions for Chapter: Applications of Derivatives, Exercise 5: Target Exercises

The function $f\left(x\right)=3{\cos }^{4}x+10{\cos }^{3}x+6{\cos }^{2}x-3, 0\le x\le \pi$ is

The values of $k$ for which the function $f\left(x\right)=k{x}^3-9x^2+9x+3$ may be increasing on $R$ are

If $f\left(x\right)=2x^3+9x^2+\lambda x+20$ is a decreasing function of $x$ in the largest possible interval $\left(-2,-1\right),$ then $\lambda$ is equal to

The value of $a$ in order that $f\left(x\right)=\sin x-\cos x-ax+b$ decreases for all real values, is given by

If $f\left(x\right)=\left\{\begin{array}{lc}3x^2+12x-1,& -1\le x\le 2\\ 37-x,& 2<x\le 3\end{array}\right.$, then

The function $y=x^3+5x^2-1$ is decreasing in the interval

Given that $f^{\text{'}}\left(x\right)>g^{\text{'}}\left(x\right)$ for all real $x$ and $f\left(0\right)=g\left(0\right),$ then

If $f^{"}\left(x\right)<0, \forall x\in \left(a,b\right)$, then $f^{\text{'}}\left(x\right)=0$