1. Find the critical numbers of the function and decide whether the critical number is an absolute maximum or absolute minimum on the interval [-6, -1], y= 2x3 + 15x2 2. Find the absolute maximum and absolute minimum values of f(x) = -x2 - 2x + 8 on the interval [-3, 2]. 3. Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x) = x3 - 2x2 - 4x +2, [-2, 2] 4. Verify that the function satisfies the hypotheses of The Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of The Mean Value Theorem. f(x) = 8x2 + 8x + 3, [-8, 8]Given f(x) = 3x4 - 4x3 - 12x2 + 5 Hint: you will need the first and second derivative for these questions! 1. For what x-value(s) do the local minima and local maxima exist? 2. On what interval(s) is the function increasing? 3. On what interval(s) is the function decreasing? 4. What is/are the local maximum value(s)? 5. What is/are the local minimum value(s)? 6. For what x-value(s) does the inflection point exist? 7. What are the point(s) of inflection? 8. On what interval(s) is the function concave up? 9. On what interval(s) is the function concave down