Pre-Calc Homework Solutions 127

Pre-Calc Homework Solutions 127 - Section 4.1 80. Use...

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Unformatted text preview: Section 4.1 80. Use implicit differentiation. x2 d 2 (x ) dx 127 Quick Review 4.1 1. f (x) 2. f (x) 3. f (x) 1 2 4 3 1/4 x 4 d 2(9 dx x d (4 dx y2 1 d (1) dx x) 2 4 1 x d 2 (y ) dx 2x 2yy y y 0 2x x 2y y d x dx y (y)(1) (x)(y ) y2 y x x y x 2) 3/2 1/2 (9 (9 x 2) 3/2 d (9 dx x 2) (9 4. f (x) x 2) d 2 (x dx ( 2x) 1/3 2x x 2)3/2 d 2 (x dx 1) 4/3 1 2 (x 3 1) 1 (2x) 1 2 (x 1) 4/3 3 2x 3(x 2 1)4/3 1) y2 y 2 5. g (x) 6. g (x) 7. h (x) y2 1 ( 3) 3 x2 1 d 2 (x dx 1) 2x x2 1 sin (ln x) x x y3 1 y3 2 sin (ln x) e 2x d 2x dx d x dx d ln x dx 2e 2x 1 . . (since the given equation is x 2 At (2, 3), d y dx 2 2 1) 1 3 3 1 y3 . 8. h (x) d ln x e dx Chapter 4 Applications of Derivatives s Section 4.1 Extreme Values of Functions (pp. 177 185) Exploration 1 Finding Extreme Values 9. As x 3 , 10. As x 11. (a) d 3 (x dx 9 9 x 2 0 . Therefore, lim f (x) x3 3 , 2x) x 2 0 . Therefore, lim 3x 2 2 2 1 f (x) x 3 f (1) (b) d (x dx 3(1)2 2) 1 1 1. From the graph we can see that there are three critical points: x 1, 0, 1. Critical point values: f ( 1) 0.5, f (0) 0, f (1) 0.5 Endpoint values: f ( 2) 0.4, f (2) 0.4 Thus f has absolute maximum value of 0.5 at x 1 and x 1, absolute minimum value of 0 at x 0, and local minimum value of 0.4 at x 2 and x 2. f (3) (c) Left-hand derivative: lim h0 f (2 h3 h) h f (2) 6h 2 h 10h lim h0 [(2 h)3 2(2 h h)] 4 lim h0 lim (h 2 h0 6h 10) [ 2, 2] by [ 1, 1] 10 Right-hand derivative: lim h0 2. The graph of f has zeros at x 1 and x 1 where the graph of f has local extreme values. The graph of f is not defined at x 0, another extreme value of the graph of f. f (2 h h h) h f (2) lim h0 [(2 h) h 2] 4 lim h0 lim 1 h0 [ 2, 2] by [ 1, 1] 1 d 3. Using the chain rule and x dx x df 1 x2 . x (x 2 1)2 dx ( ) x , we find x Since the left- and right-hand derivatives are not equal, f (2) is undefined. ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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