Mathematics - Functions Question with Solution | TestHub

$f(x)=-x^3+x^2-x+{\cos }^{-1}x$ Domain $=[-1,1]$

$f^{\prime }(x)=-3x^2+2x-1-\frac{1}{\sqrt{1-x^2}}<0$ ' $f$ ' is a decreasing function ∴ Min of $f(x)$ is $f(1)=-1+1-1+0=-1$ Max of $\mathrm{f}(\mathrm{x})$ is $f(-1)=1+1+1+\pi =3+\pi$ Range $=[-1,3+\pi ]$