AP Calculus Cheat Sheet
Name:
AP Calculus Concept Checklist
POINTS TO REMEMBER
To find the average rate of change: Find the slope of the points
Instantaneous Rate of Change : Find the Slope of Tangent Line i.e. find the derivative and substitute the given points
LIMITS AND CONTINUITY
Limits:
1. When finding limits at a number, try plugging number in first.
2. If that doesn’t work, try factoring, using common denominators, or using conjugates.
3. Left and right sided limits must be equal for limit to exist.
4. Limit approaching infinity, apply the three conditions for the degree of numerator and denominator
5. Limits from graph: Look if the limit from the left equals the limit from the right. Check if there are any breaks in the graph
Limits and Continuity:
A function [pic] is continuous at [pic] if
i). f(a) exists
ii). [pic] exists
iii). [pic]
Otherwise, f is discontinuous at x = a.
The limit [pic] exists if and only if both corresponding one-sided limits exist and are equal – that is,
[pic]
Limits of Rational Functions as [pic](Similar to Horizontal Asymptote)
i). if the degree of [pic] Example: [pic]
ii). if the degrees of [pic] Example: [pic]
iii). if the degree of [pic] Example: [pic]
DERIVATIVES
FORMULA
1. [pic] Remember:
2. Product Rule [pic] 1. Rewrite radicals as exponents
3. Quotient Rule [pic] 2. Use laws of exponents
4. [pic]
5. [pic]
6. [pic]
7. [pic]
8. [pic]
9. [pic]
10. [pic]
11. [pic]
12. [pic]
13. [pic]
14. [pic]
15. [pic] finds the derivative of [pic] at x. This WILL BE a multiple choice question.
Chain rule:
1. Derivative of the outside function times the derivative of the inside function
2. Remember the short cut for trig, ln, e
Implicit derivative:
1. When differentiating y, remember to write the dy/dx
2. The aim is to get dy/dx on one side and the other terms on the right
Steps to find the equation of the tangent:
1. Find the derivative
2. Substitute the given points to find the slope
3. Use point slope form to find the equation
Critical number: Set the first derivative equal to zero
1st Derivative Test:
1. Tells us max/min,
2. Tells us increasing/decreasing intervals
3. Tells us slope of a tangent line
4. Can be used to find velocity.
Point of inflection: Set the second derivative equal to zero
2nd Derivative Test(Concavity)
1. Tells us inflection points
2. Tells us about the concavity (>0 is concave up, ................
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