Homework SourseVerify that the function satisfies the hypotheses of the Mea
Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.
f(x)=x^3-3x+2, [-2,2]
f(x)=x^3-3x+2, [-2,2]
Solution
(f(2)-f(-2))/4 = (8-6+2+8-6-2)/4 = 1
f\'(x) = 3x^2 - 3 = 1
3(x^2 - 1)= 1
x^2 -1 = 1/3
x^2 = 4/3 = 2/3 = 2/1.732 = 1.154
x = c =
