Give the value of c in the interval [2,4] that satisfies the conclusion of the mean value theorem for :

Question

g(x) = x^2 2x 4

possible answers:

a) 3

b) 2

c) 4

d) 11/4

e) 5/2

Answer 1

the mean value theorem states, roughly, that given a section of a smooth curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.

Your equation is not clear but here is how to solve the problem

The average slope in the interval is {g(4)-g(2)}/2

set the derivative of g(x) equal to the average value and solve for x