Consider the function h(x)= cases x^2+a & x 1 x & x>1 cases defined on the closed interval

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

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}

(d)

a=2