Ximpledu

Mean Value Theorem

See how to use the mean value theorem.
1 example and its solution.

Mean Value Theorem

Theorem


If y = f(x) is continuous in interval [a, b]
and
if y = f'(x) is differentiable in interval (a, b),

then x = c exists that satisfies
f'(c) = f(b) - f(a)b - a.
f'(c): Slope of y = f(x) at x = c.
Derivative Rules

f(b) - f(a)b - a: Slope between two endpoints
(= average slope)

Example

A car passes though 10 miles in 6 minutes.
Show that the speed of the car has reached 100mph.
Solution