5 Questions
What is the equation for the mean value theorem?
$f'(c) = \ rac{f(b) - f(a)}{b - a}$
What is the mean value theorem?
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.
What is Lagrange's theorem?
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.
What is the function used in the given code?
$f(x) = x^3 - 12x - 5$
What is the interval used in the given code?
[-4, 4]
This quiz tests your understanding of the mean value theorem in calculus for engineers, specifically using MATLAB. It covers the concept of continuity, differentiability, and the existence of at least one number satisfying the mean value theorem on a closed interval.
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