Let f(x)= cases x^ 2 -4, & x 2 4x-8, & x>2 cases Determine whether there exists a…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)= \begin{cases} x^{2}-4, & x\le 2\\ 4x-8, & x>2 \end{cases}

Determine whether there exists a number

c

[0,3]

such that

f(c)=0

. Answer "exists" or "does not exist" and support your conclusion with the appropriate endpoint values.