160 test 2 derivatives revised

# 160 test 2 derivatives revised - Name Math 160 Test#2...

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Name: __________________ Math 160 Test #2: Limits, Continuity and Derivatives Find the derivative of the function: 1. 10 6 ) ( x x f = 2. ) ln( ) ( t t h = 3. k ke k m 5 ) ( = 4. 10 10 ) ( t t r t + = 5. ) ( log ) ( 2 s s p = 6. 3 ) ( x x g = 7. 3 1 ) ( t t s = 8. π = ) ( x C 9. 2 5 2 ) ( 2 - + = r r r r Q 10. ) 4 2 ln( ) ( 2 + + = x x x M 11. State the definition of the derivative of the function f ( x ). Use the definition to find the derivative of the function 1 5 ) ( 2 + - = x x x f What is the equation of the line tangent to the graph of this function at x = 2?

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12. The slope of the secant line to the graph of g ( x ) between x = 5 and x = 5 + h is 10 – 6 h + 2 h 2 . What is the slope of the tangent line at x = 5? 13. Let f ( x ) be a function with x -intercepts at x = 2 and x = -4 and with horizontal tangents at x = 3 and x = 5. Additionally, g ’(1) = 1 and g (0) = 1. Let g ( x ) be ln( f ( x )). At what point(s) does g have a horizontal tangent? 14. If the marginal profit for manufacturing widgets is -\$20/widget, what does this mean? In order to maximize profit, would you recommend that the company manufacture more or fewer widgets?
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