Calculus Formulas Power Rules: xn =nxn−1 dx d and ∫ + + = + c n x x dx n n 1 1 Product Rule: []f ()x g x f () ()x g x f x g x dx d ⋅ = ⋅ ' + ' ⋅ Quotient Rule: () () ()( ) []()2 ' ' g x g x f x f x g x g x f x …

This Calculus Handbook was developed primarily through work with a number of AP Calculus classes, so it contains what most students need to prepare for the AP Calculus Exam (AB or BC)

1) If f x changes from negative to positive at c, then f c is a relative minimum of f. 2) If f x changes from positive to negative at c, then f c is a relative maximum of f.

____________________________________________________________________________________ First Derivative Test: Let c be a critical number of the function f that is continuous on an open …

Basic Properties and Formulas If fx and g x are differentiable functions (the derivative exists), c and n are any real numbers, 1. cf cf x

Basic Properties and Formulas TEXAS UNIVERSITY CASA CENTER FOR ACADEMIC STUDENT ACHIEVEMENT

1. Find all critical points of fx( ) in [ab,]. 2. Evaluate fx( ) at all points found in Step 1. 3. Evaluate fa( ) and fb( ). 4. Identify the abs. max. (largest function value) and the abs. min.(smallest …

Fundamental Theorem of Calculus: Suppose 𝑓𝑓(𝑥𝑥) is continuous on [𝑎𝑎,𝑏𝑏], then Part I: ∫𝑙𝑙(𝑥𝑥) ( =∫𝑓𝑓(𝑡𝑡)𝜋𝜋𝑡𝑡

Quadratic Formula If , then . Inequalities and Absolute Value If and , then . If , then . If and , then . If and , then . If , then means or means means or GEOMETRY Geometric Formulas Formulas …

Fundamental Theorem of Calculus: ' x a d F xftdtfx dx where f t is a continuous function on [a, x]. b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). Riemann Sums: 11 nn ii ii ca c a 111 nnn …

To compute p(x) lim factor largest power of x in q(x) out of x! 1 q(x) both p(x) and q(x) then compute limit. 1 exist. If the two one sided limits had been equal x2 then lim g(x) would have …

67. linearization formula L (x) f (a) f (a) (x a) 68. Newton’s Method x x f x n f x n n 1 bg bg 69. k f u du k f u du 70. z f (u ) g(u ) du z f (u )du z g 71. Mean Value Theorem If f is continuous on ab,, …

1) If f x changes from negative to positive at c, then f c is a relative minimum of f. 2) If f x changes from positive to negative at c, then f c is a relative maximum of f.

Let f be defined at c. If f c 0 or if f is undefined at c, then c is a critical number of f. _______________________________________________________________________ First …

Formulas and Theorems 1a. Definition of Limit: Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number. Then f x L means that for each x …

Integration Formulas Z dx = x+C (1) Z xn dx = xn+1 n+1 +C (2) Z dx x = ln|x|+C (3) Z ex dx = ex +C (4) Z ax dx = 1 lna ax +C (5) Z lnxdx = xlnx−x+C (6) Z sinxdx = −cosx+C (7) Z cosxdx = …

The Fundamental Theorem of Calculus: Fresh Take. Integration Formulas and the Net Change Theorem: Learn It 1 ... If no domain is stated for a function [latex]y=f(x)[/latex], the domain is …

_____________________________________________________________________________________________________ Intermediate Value Theorem: If f is continuous on [a, b] and k is any number between f (a) and …