Mean Value Theorem Quiz

$f'(c) = \rac{f(b) - f(a)}{b - a}$

The mean value theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the instantaneous rate of change of the function is equal to the average rate of change of the function over the closed interval.

Lagrange's theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the instantaneous rate of change of the function is equal to the slope of the secant line connecting the endpoints of the interval.

<p>$f(x) = x^3 - 12x - 5$</p> Signup and view all the answers

<p>[-4, 4]</p> Signup and view all the answers