Mathematics

Problem

Consider the function

h(x)=\begin{cases} x^2+a & x\le 1 \\ \sqrt{x} & x>1 \end{cases}

defined on the closed interval

[0,4]

. For which value of the constant

a

will Rolle's Theorem guarantee the existence of a number

c

(0,4)

such that

h'(c)=0

? a)

a=0

b) No real value of

a

satisfies the hypotheses c)

a=-\dfrac{3}{2}

a=2