A function is continuous on and differentiable on with

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

Problem

A function

h

is continuous on

[0,5]

and differentiable on

(0,5)

with

|h(5)-h(0)|\le 7

. Which of the following is the largest number

K

such that one can guarantee the existence of

c

(0,5)

with

|h'(c)|\le K

? (a)

7

(b)

\dfrac{5}{7}

(c)

\dfrac{7}{5}

(d) Cannot be determined from the given information