Homework 6

# Homework 6 - MATH 106 CALCULUS I FOR BIO. & SOC. SCI....

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Unformatted text preview: MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Homework 6. Due date Wednesday October 19, 2011 Please show all your work. (1) (5 Points) Suppose that f and g are differentiable functions such that f (1) = 2 , f (2) = 1 , f ′ (1) = − 2 , f ′ (2) = − 1 g (1) = − 2 , g (2) = 2 , g ′ (1) = 3 , g ′ (2) = 1 . (a) If a ( x ) = f ( √ x ) compute a ′ (1). (b) If b ( x ) = radicalbig f ( x ) compute b ′ (1). (c) If c ( x ) = f ◦ f ( x ) compute c ′ (1). (d) If d ( x ) = f ◦ g ( x ) compute d ′ (2). (e) If e ( x ) = f ( x ) g (2 x ) compute e ′ (1). (2) (10 Points) Compute the derivatives of the following functions. (a) (2 Points) a ( x ) = radicalBig x 2 + √ 2 x + 5 . (b) (2 Points) b ( t ) = parenleftbigg cos(2 x ) ( x + 3) 2 parenrightbigg 3 (c) (2 Points) c ( x ) = radicalbigg x 2 / 3 + 1 x 2 / 3 . (d) (2 Points) If d ( x ) = ( x 4 − x ) 3 / 2 find d ′′ (2)....
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## This note was uploaded on 01/20/2012 for the course CALC AS.110.106 taught by Professor Josegomez during the Fall '11 term at Johns Hopkins.

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Homework 6 - MATH 106 CALCULUS I FOR BIO. & SOC. SCI....

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