The total cost (in dollars) to manufacture cell-phone cases is modeled by a…

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

Problem

The total cost

C(x)

(in dollars) to manufacture

x

cell-phone cases is modeled by a differentiable function. If

C(500)=10\,000

and

C(800)=14\,200

, which of the following statements is necessarily true? (a) For all

x

between 500 and 800,

C'(x)=14

. (b) For some

x

between 500 and 800,

C'(x)=\dfrac{14\,200}{800}

. (c) For some

x

between 500 and 800,

C'(x)=14

. (d) For some

x

between 500 and 800,

C'(x)=\dfrac{14\,200-10\,000}{800}