Chapter42007

# Calculus: Early Transcendental Functions

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Unformatted text preview: Chapter 4 Test October 29, 2007 1. Find the x - coordinate of the absolute minimum of Ä 2. f HxL = x ÄÄ5ÄÄ Hx + 1L 3 Name f HxL = x3 - x2 - x + 1 on the interval @- 2, 2D. Justify your answer. Find all critical values for the function Hx - values only, from the first derivativeL. 3. f HxL = 3 x e2 x Use the Second Derivative Test to find all local extreme values Hx - values onlyL for the function on the interval H-•, • L 4. f HxL = cos-1 x Find the number HsL c that satisfies the Mean Value Theorem on the interval @- 1, 1D. 5. f HxL = cos 2 x - 2 sin x Find where the function is increasing and decreasing on the interval HHint : make use of a trig identityL 6. f HxL = x2 - 4 x + 6 If x1 = 1, use Newton¢ s Method to find x2 and x3 . 7. If the derivative of a function is defined as concave down on the interval H-•, •L. 8. f HxL = x 2 x @0, 2 pD f ¢ HxL = x H1 - x2 L 3 , Find the linearization L HxL for f HxL at a = 2. 1 ÄÄÄÄÄ then find where the graph of f HxL is concave up and 9. Find dy if 10. If f HxL = y = cot2 H2 xL, then evaluate dy for sin x, 1, 1 ÄÄÄÄÄ x2 - p, p Find HaL lim+ f ¢ HxL xÆp p x = ÄÄÄÄÄ 6 and -1 dx = ÄÄÄÄÄÄÄÄÄÄ . 2 x<p x=p x>p f Hp + hL - f HpL HbL lim- f ¢ HxL HcL lim + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ Ä xÆp hÆ0 h f Hp + hL - f HpL HdL lim - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ Ä hÆ0 h 11. Atticus is in a rowboat 3 miles from a straight coast. He wants to go to Boo Radley ¢ s house 2 miles down the coast Hsee diagram on white boardL. Atticus can row at 4 mph and jog at 6 mph. Where should he land on the coast in order to arrive at Boo' s house in the shortest possible time? 12. A 12 - foot ladder leans against the side of a house. The base of the ladder is pushed toward the house at a rate of 2 feet per second. When the bottom of the ladder is 3 feet from the house Hsee diagram on white boardL, find how fast the top of the ladder is moving up the side of the house. 13. Find the point HsL on the parabola 1 y = ÄÄÄÄÄ x2 - 2 2 that is ê are closest to the origin, H0, 0L. 1 14. The graph of f HxL is shown. Draw the graph of ÄÄÄÄÄ f H2 x + 4L + 1, on the same set of coordinate axes. 2 5 4 3 2 1 −4 −3 −2 −1 −1 −2 1 2 3 4 5 6 ...
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