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20 minutes

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1.

2. Find a positive value c, for x, that satisfies the conclusion of the Mean Value Theorem for Derivatives for f(x) = 3x^{2} - 5x + 1 on the interval [2, 5].

3. Given f(x) = 2x^{2} - 7x - 10, find the absolute maximum of f(x) on [-1, 3].

4. Find If x^{3}y + xy^{3} = -10.

5.

6.

7. Find the equation of the tangent line to 9x^{2} + 16y^{2} = 52 through (2, -1).

8. A particle's position is given by s = t^{3} - 6t^{2} + 9t. What is its acceleration at time t = 4 ?

9. If f(x) = 3^{πx}, then f′(x) =

10. The average value of f(x) = from x = 1 to x = e is