Consider the function for

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

Problem

Consider the function

g(x)=\dfrac{x^{2}-9}{x-3}

for

x\neq 3

. On the closed interval

[0,3]

, does the Mean Value Theorem apply? (a) Yes, because

g

can be simplified to

g(x)=x+3

, which is continuous and differentiable on

[0,3]

. (b) No, because

g

is not differentiable at

x=0

, an endpoint of the interval. (c) No, because

g

is not continuous at

x=3

, an endpoint of the interval. (d) Yes, because the discontinuity at

x=3

is removable, so it does not affect the theorem.