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practice-quiz4 - f ′ x and f ′′ a 8 If f x =(2 x...

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AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Practice Problems for Quiz # 4 1. Find the equation of the tangent line to the curve y = 4 x 3 + 1 at the point (2,33). 2. Find the equation of the tangent line to the curve y = 2 x 2 - 5 x + 3 at the point where x = 3. 3. Evaluate the limit lim x →∞ 5 x 3 - 2 x 2 + 7 2 x - 4 x 2 - 7 x 3 4. The graph of f ( x ) is shown below. At which of the marked points is (a). f ( x ) the least? (b). f ( x ) the greatest? (c). f ( x ) the least? (d). f ( x ) the greatest? (e). f ′′ ( x ) the least? (f). f ′′ ( x ) the greatest? x f’(x) A B C D 5. If f ( x ) = 23 x 4 , find f (2). Also find f ′′ (1). 6. If h ( b ) = ab + b 2 - 23 b 3 , find h (2). Also find h ′′ ( a ). 7. If f ( y ) = 6 y 2 - 12 e y + x 2 , find
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Unformatted text preview: f ′ ( x ) and f ′′ ( a ). 8. If f ( x ) = (2 x 2-3)(2 x + 3), ±nd f ′ ( x ). 9. If s ( a ) = − 9 x 3 √ a , ±nd s ′ ( x ). 10. Let g ( x ) = 6 x 5 √ x + 3 x 6 √ x . Find g ′ ( x ). 11. Let f ( x ) = √ 3 x + 7 + 4 x + 1 3 x 2 . Find f ′ ( x ). 12. A car moves along a straight road and its position at time t is given by s ( t ) = 2 t 3-20 t 2 +100 t . Find the velocity of the car at time t = 0. At which times is the car at rest? What is the total distance travelled by the car between time t = 0 and t = 20?...
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