Review your knowledge of the mean value theorem and use it to solve problems.

What is the mean value theorem?

The mean value theorem connects the average rate of change of a function to its derivative. It says that for any differentiable function f and an interval open bracket, a, comma, b, close bracket (within the domain of f), there exists a number c within left parenthesis, a, comma, b, right parenthesis such that f, prime, left parenthesis, c, right parenthesis is equal to the function's average rate of change over open bracket, a, comma, b, close bracket.
Graphically, the theorem says that for any arc between two endpoints, there's a point at which the tangent to the arc is parallel to the secant through its endpoints.
Want to learn more about the mean value theorem? Check out this video.

Check your understanding

Problem 1
f, left parenthesis, x, right parenthesis, equals, x, start superscript, 3, end superscript, minus, 6, x, start superscript, 2, end superscript, plus, 12, x
Let c be the number that satisfies the Mean Value Theorem for f on the interval open bracket, 0, comma, 3, close bracket.
What is c ?
Choose 1 answer:
Choose 1 answer:

Want to try more problems like this? Check out this exercise.