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Unformatted text preview: f ( x ) = x  x  is diﬀerentiable and ﬁnd a formula for f . 12. Diﬀerentiate the function y = 6 x8 / 3 . 13. Find all points on the curve y = x 3 + 3 x 2 + 3 x + 1 where the tangent is horizontal. 14. Diﬀerentiate ( x 3 + 1) e x . 15. Diﬀerentiate e x1 e x + 1 . Answers: 1. x ≥ 4 2. Graph should come down to (1 , 0), then go back up and come down again at (1 , 0), then go up again. At these 2 points the graph should have “corners”. 3. x = log( y ) 2 4.∞ 5.3 6. c =2 7. x = 1 8. 4 9. y1 = 3( x1) or y = 3 x2 10. Graph of function should pass though (0 , 0) and (1 , 0) and should slope down at both these points. 2 11. All x , derivative is 2  x  . 12.16 x11 / 3 . 13. ( x, y ) = (1 , 0). (Accept just x =1 as correct.) 14. ( x 3 + 3 x 2 + 1) e x . 15. 2 e x / ( e x + 1) 2 3...
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 Fall '08
 WILKENING
 Math, Calculus, Derivative, Continuous function, clear correct answer

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