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Question 1
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Consider the function $$f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\leq4} \\ {{e}^{-x},} & {if\, x{\gt}4}\end{cases}$$ Which of the following statements about f(x) is true:
A.
f(x) has a local maximum at x =1, which is also the global maximum
B.
f(x) has a local maximum at x=2, which is not the global maximum
C.
f(x) has a local maximum at $x =\pi$, but it is not the global maximum
D.
f(x) has a global maximum at x=0
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