Review Test#2 - h t 16 t 2 80 t feet When will it reach its...

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Math 131 Test #2 will stress the material since the last test; so we start with problems on limits and end with derivatives & graphing. Study class notes and webassigns. Here are some problems off of other teacher’s old tests for extra practice. 1. Find the derivative of y = 3 x + 1 and y = ! 1 2 x 2 . 2. Determine all values of x where relative extrema of the function, f ( x ) = 1 3 x 3 ! 3 2 x 2 ! 10 x occur. Distinguish the maxima from the minima using the second derivative rule or the first derivative rule. Show your reasoning and which rules you are using. 3.Determine the minimum value of f ( x ) = x + 1 x ! 1 for x > 1. 4. Sketch the graph of f ( x ) = 1 4 x 4 ! x 3 + 2 ; be sure to show how you are using derivatives to find all extrema and inflection points. Clearly label your graph. 5. Suppose a ball is thrown into the air and after t seconds has height
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Unformatted text preview: h ( t ) ! 16 t 2 + 80 t feet. When will it reach its maximum height? 6. Compute the limit a. lim x !" 2 x + 1 x + 2 b. lim x !" 2 x + 1 x 3 + 2 c. lim x !" 2 x 4 + 1 x + 2 d. lim x !" x # 3 x 2 # 9 e. lim x ! 3 x " 3 x 2 " 9 7. Suppose f (50) = 25 and ! f (50) = 2 estimate f(52) and f(49) Estimate g(51) if g ( x ) = f ( x ) 8.Differentiate the following a. f ( x ) = 6 2 x 3 + x b. y = x 5 + 5 x c. f ( x ) = ( 3 x + 5) 2 9. Suppose the position of a car at time t is given by s ( t ) = 50 t ! 7 t + 1 . Find the velocity and acceleration of the car at t=0/ 10. Use the methods we have studied to draw the graph of the function y = t 3 ! 3 t 2 + 5 on the interval [-1/2, 4 ]...
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