1205_T3_sampleAns - Math 1205 Test 3 1[14 Given f Hx L = x2...

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Math 1205 -- Test 3 25 Apr 2007 NAME: You will be graded on how well and fully you support your work! Use only methods developed in class. 1 . [14] Given f H x L = è!!!! x 3 H x + 4 L a. Determine all critical points for f H x L . f ' H x L = 2 x + 4 ÅÅÅÅÅÅÅÅÅÅÅÅÅ "####### x 2 3 (use the product rule). f ' H x L DNE when x = 0 f ' H x L = 0 when x = - 2 b. Determine the absolute maximum and absolute minimum of f H x L on the interval @ - 2, 0 D . Evaluate f H x L at the critical points AND the endpoints: f H - 2 L = - 2 è!!!! 2 3 f H 0 L = 0 ABSOLUTE MAX: 0 ABSOLUTE MIN: - 2 è!!!! 2 3 2 . [14] Can the Mean Value Theorem be applied to the function f H x L = x 2 + 2 x - 1 on the interval [0, 1]? Why or why not? If the Mean Value Theorem can be applied, find all values of c that satisfy the theorem. Yes, the Mean Value Theorem can be applied to f H x L since f H x L is continuoud on [0,1] and differentiable on (0,1). So, there exists some c in [0,1] where f ' H c L = f H b L - f H a L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅ b - a = f H 1 L - f H 0 L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ 1 - 0 = 2 - H - 1 L
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