The function is defined on by k(x)= cases x^2+3x,&-3 x 1, 7-2x,&1<x 6

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The function

k

is defined on

[-3,6]

k(x)=\begin{cases}x^2+3x,&-3\le x\le 1,\\7-2x,&1<x\le 6.\end{cases}

In one or two sentences, explain why

x=1

must be included among the candidate points when determining the absolute extrema of

k

on the interval.