CalcExercisesCh4

# CalcExercisesCh4 - (Exercises for Section 4.1: Extrema)...

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(Exercises for Section 4.1: Extrema) E.4.1 CHAPTER 4: APPLICATIONS OF DERIVATIVES SECTION 4.1: EXTREMA 1) For each part below, find the absolute maximum and minimum values of f on the given interval. Also give the absolute maximum and minimum points on the graph of y = fx () . Show work! a) = 15 + 8 x ± 2 x 2 on ± 1, 3 ² ³ ´ µ b) = 1 4 x 4 ± 5 3 x 3 ± 3 x 2 + 10 on ± 1, 2 ² ³ ´ µ c) = x 2 ± 16 x on ± 4, ± 1 ² ³ ´ µ 2) For each part below, find the domain and the critical number(s) (“CNs”) of the function with the indicated rule. If there are no critical numbers, write “NONE.” a) = 4 x 4 ± x 3 ± 32 x 2 + 12 x + 13 b) gt = t 2 ± 36 c) hx = x 4 x ± 1 d) p ± = 1 2 cos 2 + sin e) qx = cot x

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(Exercises for Section 4.2: Mean Value Theorem (MVT) for Derivatives) E.4.2 SECTION 4.2: MEAN VALUE THEOREM (MVT) FOR DERIVATIVES 1) For each part below, determine whether or not f satisfies the hypotheses of Rolle’s Theorem on the given interval a , b ± ² ³ ´ . If it does not, explain why not. If it does, find all real values c in a , b () that satisfy the conclusion of the theorem; i.e., ± fc = 0 . a) fx = x 2 ± 6 x + 10 on 1, 5 ± ² ³ ´ b) = x 2 ± 6 x + 10 on 3, 7 ± ² ³ ´ c) = x 4 + 14 x 3 + 69 x 2 + 140 x ± 5 on ± 6, ± 1 ² ³ ´ µ ; Hint: ± 2 is a value for c that satisfies ± = 0 . d) = x on ± 4, 4 ² ³ ´ µ 2) For each part below, determine whether or not f satisfies the hypotheses of the Mean Value Theorem (MVT) for Derivatives on the given interval a , b ± ² ³ ´ . If it does not, explain why not. If it does, find all real values c in a , b that satisfy the conclusion of the theorem; i.e., ± = fb ² fa b ² a . a) = x + 4 x on 1, 4 ± ² ³ ´ b) = 2 x 3 + 5 x 2 ± 4 x + 3 on ± 2, 3 ² ³ ´ µ c) = x 2/3 on ± 8, 8 ² ³ ´ µ d) = 3 x + 1 on 0, 2 ± ² ³ ´ KNOW THE FOLLOWING • Rolle’s Theorem • The Mean Value Theorem (MVT) for Derivatives
(Exercises for Section 4.3: First Derivative Test) E.4.3 SECTION 4.3: FIRST DERIVATIVE TEST 1) For each part below, sketch the graph of y = fx () . • Find the domain of f . • State whether f is even, odd, or neither, and incorporate any corresponding symmetry in your graph. • Find the y -intercept, if any. You do not have to find x -intercepts. • Find and indicate on your graph any holes, vertical asymptotes (VAs), horizontal asymptotes (HAs), and slant asymptotes (SAs), and justify them using limits. • Find all points at critical numbers (if any). Indicate these points on your graph. • Use the First Derivative Test to classify each point at a critical number as a local maximum point, a local minimum point, or neither. (The next instruction may help.) • Find the intervals on which f is increasing / decreasing, and have your graph show that. a) = x 4 + 14 x 3 + 69 x 2 + 140 x ± 5 . Hint 1: You studied this in Section 4.2, Exercise 1c.

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## This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

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CalcExercisesCh4 - (Exercises for Section 4.1: Extrema)...

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