For problems 1 - 3, find the indicated. 1. Find the absolute minimum and absolute maximum values of the function f(x)=x*on [-2,2]. 2. A ladder 15 feet long leans against a house. The base of the ladder is pulled away from the wall at a rate of 4 ft/sec. How fast is the top of the ladder moving down the wall when its base is 4 feet from the wall? (Hint: start with x% + y? = 152 where x, y are functions of t.) 3. Determine all the numbers which satisfy the conclusions of the Mean Value Theorem for the function f(x) = x* + 2x? x on [1, 2]. For problems 4 -6, let f(x) = 2x3 9x% 60x 4. |dentify the critical points of the function f. 5. Determine the intervals on which the function increases and decreases. 6. Classify the critical points as relative maximums, relative minimums or neither. For problems 7 -8, let f(x) = x* 2x* 12x2. 7. Find the second derivative of f and determine the intervals on which the function is concave up and concave down. 8. Determine the inflection points of the function. For problems 9 10, find the indicated. 9. Find the indefinite integral: [ (2x? + =) dx 10. Evaluate the definite integral: [ 5 Vi dx