Calculus Exam Review: Mean Value Theorem and Rolle's Theorem

These flashcards cover key vocabulary and concepts related to the Mean Value Theorem, Rolle's Theorem, and related topics in calculus.

Mean Value Theorem

Suppose f is continuous on closed bounded interval [a,b]. F is differentiable on open bounded interval (a,b). There is some c on (a,b). F’(C) = f(b)-f(a)/b-a

Rolle's Theorem

Suppose f is continuous on closed bounded interval [a,b]. F is differentiable on open bounded interval (a,b). There is some c on (a,b). F’(C) = 0.

Average Rate of Change Formula

(f(b) - f(a)) / (b - a)

Critical Points

Values of x where the derivative is zero or undefined, indicating potential local maxima or minima.

First Derivative Test

A method used to determine the intervals on which a function is increasing or decreasing by analyzing the sign of its first derivative.

Inflection Point

A point on a curve where the concavity changes, determined by the second derivative changing its sign.

Crit points

Find derivative
Factor
x = 0,(factor 1)(factor 2)

End points

[a,b]

Implicit differentiation

Derivative
Set y to dy/dx
set to equal dy/dx

logarithmic differentiation

Multiply everything by ln
change root to power
move power to front
simplify
multiply new function with old one