Question

Let the function $f(x)$ be defined as follows
$f(x)=\begin{cases}x^{3}+x^{2}-10 x, & -1 \leq x<0 \\ \cos x, & 0 \leq x<\pi / 2 \\ 1+\sin x, & \pi / 2 \leq x \leq \pi\end{cases}$
Then $f(x)$ has

• A. a local minimum at $x=\pi / 2$
• B. a global maximum at $x=\pi / 2$
• C. an absolute minimum at $x=-1$
• D. an absolute maximum at $x =\pi$

Answer 1

Answer: (C)

Correct answer is (c) an absolute minimum at $x=-1$