Question

Use the graph of f(x) = |x(x2 − 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the Mean Value Theorem.

Answer 1

1 time

Explanation:

f(x) = |x(x^2 − 1)|

The mean value theorem states

f'(c) = f(b) -f(a)

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b-a

b = .75

a = .5

f(b) = abs(.75 * (.75^2 -1)) = abs (.75*(-.4375))=abs(-.328125)

= .328125

f(a) = abs(.5 * (.5^2 -1)) = abs(.5*(-.75))=abs(-.375) = .375

.328125- .375

f'(c) = -------------------------------------------------

.75-.5

f'(c) = -.1875