Calculus 1 Hour Exam 2 - Math 221 Fall, 2011

1.	Find the function f(x) with f ‘’(x) = 6x + 2 and f(0) = 4, f ‘(1) = 6. Answer: f(x) = x^3 + x^2 + x + 4
2.	Give the definition of critical number (sometimes called critical point). Answer: An x-value where f ‘(x) = 0 or f ‘(x) is undefined.
3.	For each part, find f ‘(x) a. f(x) = √( 1 + 2 e^2x ) b. f(x) = x^sinx c. f(x) = (tan^-1 x)^2 Answers: a. 2 e^2x / √(1 + 2 e^2x ) b. x^sinx [ (cos x) ln x + sin x / x ] c. 2 (tan^-1 x) ( 1 . ( 1 + x^2 )
4.	Find each limit. You may use any method. Show your work or briefly explain you Reasoning – no credit given for an answer alone. a. lim ln x / √x x→∞ b. lim sin x / (1 – cos x) x→∞
5.	State the Extreme Value Theorem. Be sure to include hypothesis (“if”) and conclusion “then”). Answer: If f is continuous on [a,b], then f attains an absolute maximum and an absolute minimum on [a,b]. Click here to continue with this exam.

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