AP Calc Sem 1 Review

A rule for differentiating problems involving compositions of functions

• Chain Rule

• Implicit Differentiation

• Product Rule

• Quotient Rule

A method for finding the derivative of an implicitly defined function or relation in which the dependent variable is not isolated on one side of the equation

• Implicit Equation

• Explicit Equation

• Explicit Differentiation

• Implicit Differentiation

A theorem that states if f is a function that is continuous on the closed interval [a, b] and d is any number between f(a) and f(b), then there must be at least one number c, where a < c < b, such that f(c) = d

• The Squeeze Theorem

• The Intermediate Value Theorem (IVT)

• The Limit Theorem

• The Pythagorean Theorem

A discontinuity at which the limit of the function does not exist because both one-sided limits exist but have different values

• Infinite Discontinuity

• Removable Discontinuity

• Jump Discontinuity

• Vertical Discontinuity

The rate at which one quantity is changing by relating it to other quantities whose rates are known

• Average Rate of Change

• Instantaneous Rate of Change

• Rate of Change

• Related Rates

To say that a function f is differentiable at x means that

• f'(x) exists

• f'(x) doesn't exist

• f(x) exists

• f(x) doesn't exist

This formula is used for which of the following?

• instantaneous rate of change

• slope of a secant line equation

• average rate of change

• average velocity formula

find the slope of the tangent line means

• find the derivative
• rise over run (change in y / change in x)
• average rate of change

the slope of a tangent line equals the slope

• of the curve at that point
• average rate of change
• differentiation

slope of the tangent line formula can also be used for what?

• instantaneous rate of change 
• average rate of change
• average velocity (over an interval)