For on the interval

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

Problem

For

f(x)=|x|

on the interval

[-1,1]

, why does no point

c\in(-1,1)

satisfy

f'(c)=\dfrac{f(1)-f(-1)}{1-(-1)}

? (a)

f

is not differentiable at the endpoints

x=-1

and

x=1

(b) Because

f'(x)

(-1,1)

is either

1

-1

, it can never equal the required average rate of change

0

(c)

f

is not differentiable at

x=0

(d)

f

is not monotonic on the interval

[-1,1]