Mathematics

Problem

Let

f(x)=\begin{cases}x^2-4, & x\le 1,\\ ax+b, & x>1,\end{cases}

where

a

and

b

are real constants. a. Determine all ordered pairs

(a,b)

for which

f

is continuous on the closed interval

[-2,3]

. b. For each pair

(a,b)

you found in part (a), justify that there exists at least one number

c

[-2,3]

satisfying

f(c)=0