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AP CALCULUS AB REVIEW
Chapter 2
Differentiation
Definition of c) is a minimum
If f’’(c) < 0, then f(c) is a maximum
*Points of Inflection (take second derivative and set it equal to 0, solve the equation to get x and plug x value in original function)
*Asymptotes (horizontal and vertical)
*Limits at Infinity
*Curve Sketching (take first and second derivative, make sure all the characteristics of a function are clear)
♫ Optimization Problems
*Newton’s Method (used to approximate the zeros of a function, which is tedious and stupid, DO NOT HAVE TO KNOW IF U DO NOT WANT TO SCORE 5)
Chapter 4 & 5
Integration
*Be able to solve a differential equation
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*Basic Integration Rules
1)undu= un+1n+1+ C, n≠-1
2)sinudu= -cosu+ C
3)cosu du= sinu+ C
4)1u du= lnu
*Integral of a function is the area under the curve
*Riemann Sum (divide interval into a lot of sub-intervals, calculate the area for each sub-interval and summation is the integral).
*Definite integral
*The Fundamental Theorem of Calculus
If a function f is continuous on the closed interval [a, b] and F is an anti-derivative of f on the interval [a, b], then
abfx