mid2revmath16A

# mid2revmath16A - h x = x 5-10 x 2 14 Consider the function...

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Math 16A (Fall 2007) Kirkbride Midterm 2 Review *Note: Be sure to understand ALL problems from the homework. These are just some selected practice problems. Derivatives: Find the derivative of the following functions: 1. f ( x ) = x 8 - 3 x 6 + 500 10 - x 2 3 + 1 x + 8 2. f ( x ) = (2 x - 5) 2 x 3. f ( x ) = ( x 2 + 1 x ) 5 4. f ( x ) = (3 x 3 + 7) 2 ( x 2 - 2 x ) 5. f ( x ) = x 2 + x - 1 sin x - 1 6. f ( x ) = 2 x 2 - 3 cos x 7. f ( x ) = ( x 2 - 1)(8 x + 1 x )( x 3 + 2 x ) 8. f ( x ) = csc 3 x + cot 3 x 9. Given f ( x ) = 5 x 4 - 6 x 2 + cos 2 x , ±nd f ′′′ ( x ) Average/Instantaneous Rate of Change 10. Find the average rate of change of the function over the given interval. Then compare with the instantaneous rate of change at the endpoints. f ( x ) = x 3 + x, [ - 2 , 2] 11. Also think about word problems like 41-46 on page 167 from the Chapter 2 Review Exercises

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Graphing functions 12. Find when f’(x) = 0 and use a sign chart to ±nd the relative extrema of the function f ( x ) = 1 4 x 4 - 8 x. 13. Determine the intervals on which the graph of the following function is concave up or concave down,
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Unformatted text preview: h ( x ) = x 5-10 x 2 . 14. Consider the function f ( x ) = x 3-3 2 x 2 a) Find any/all relative extrema (use a sign chart) b) Find any/all points of in²ection (use a sign chart) c) Find any/all x and y intercepts d) Find any/all horizontal and vertical asymptotes (use limits) e) Sketch the graph of this function 15. Consider the function f ( x ) = 2 x 1 + x 2 a) Find any/all relative extrema (use a sign chart) b) Find any/all points of in²ection (use a sign chart) c) Find any/all x and y intercepts d) Find any/all horizontal and vertical asymptotes (use limits) e) Sketch the graph of this function Also review marginal pro±t, revenue, and cost, as well as velocity and acceleration. Some suggested review problems to look at Chapter 2 Review Exercises pg. 169, 47-56, 89, 90, 100...
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mid2revmath16A - h x = x 5-10 x 2 14 Consider the function...

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