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.

1 time

Step-by-step explanation:

f(x) = |x(x^2 − 1)|

The mean value theorem states

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

         -------------

           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

its a straight line parallel to the time axis