AP

MATHEMATICS · Multi correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let f(x)={x2+4x,−3≤x≤0−sin⁡x,0<x≤π2−cos⁡x−1,π2<x≤πf(x)=\begin{cases}x^2+4x,&-3\le x\le0\\-\sin x,&0<x\le\frac{\pi}{2}\\-\cos x-1,&\frac{\pi}{2}<x\le\pi\end{cases}. Then, (1) x=−2x=-2 is a point of global minimum. (2) x=πx=\pi is a point of global maximum. (3) f(x)f(x) is non-differentiable at x=π2x=\frac{\pi}{2}. (4) f(x)f(x) is discontinuous at x=0x=0.

Related theory

Browse the problem library