review - y . Check your answers for this question by...

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MAT 125 Exam 2 Review Released November 3, 2010 1. Find the derivatives of the following functions. (a) sin( x 2 e x ) (b) arctan( 5 x + 4) (c) ln ± x + 2 3 x + 4 ² (d) e sin( x )+cos( x ) (e) e x + e - x e x - e - x (f) x 2 + 4 x + 3 x 3 + 1 (g) arcsin 1 + x 1 - x (h) log 6 ( x 2 + 5 x ) (i) 5 3 x +sec( x ) 2. Find the fourth derivative of x sin x . 3. Find an equation to the tangent line of the equation x 3 y + y 3 x = 30 at the point (1 , 3). 4. Here we have drawn the graph of the function y = 2 x 3 - 3 x 2 - 12 x + 7. (a) Draw the graph of y 0 and y 00 from the graph . (b) Identify from the graph the intervals upon which y is increasing, decreasing, concave up, and concave down. Using the formula for y , verify your answers. - 15 - 10 - 5 5 10 15 - 2 - 1 1 2 3 5. Using the formula for the function in Question 4, do the following. (a) Find the intervals on which y is increasing and decreasing. (b) Find the intervals on which y is concave up and concave down. (c) Find the extreme values for y on the interval [ - 5 , 5], as well as the points where the extreme values are attained. (d) Find the points of inflection for
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Unformatted text preview: y . Check your answers for this question by examining the graph in Question 4. 1 6. A child is ying a kite. If the kite is 90 feet above the childs hand level and the wind is blowing it on a horizontal course at 5 feet per second, how fast is the child paying out cord when 150 feet of cord is out? 7. A student is driving twenty miles from his home to class theres a test today! The distance the student has driven from home is given by the function s ( t ) = 40 t-10 sin(4 t ) , t . 5 , where t is measured in hours and s is measured in miles. (a) Calculate the students velocity, acceleration, and jerk twenty minutes into the trip. (b) (Bonus, for lim x cos x-1 x extra credit!) Is the student late for the test? (Hint: Find his maximum velocity.) 2...
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This note was uploaded on 11/04/2010 for the course MAT 125 taught by Professor Bianculli during the Fall '08 term at SUNY Stony Brook.

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review - y . Check your answers for this question by...

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