Calculus:

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10. [0.08/0.09 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 3.3.037.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHE This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Suppose the derivative of a function fis f'(x) = (x + 3)4(x - 4)5(x - 5)6. On what interval is f increasing? Step 1 For any value of x * -3, the even-power term (x + 3)4 is positive positive Step 2 For any value of x # 5, the even-power term (x - 5) is positive positive Step 3 Therefore, the sign of the product (x + 3)4(x - 4)5(x - 5)6 = f'(x) depends only on the sign of (x - 4)5 (assuming x * -3). If x 4, then (x - 4) is positive , and so the sign of (x + 3)4(x - 4)5(x - 5)6 = f'(x) is positive (again assuming x * -3). Therefore, f(x) is increasing Therefore, f is increasing on the following interval. (Enter your answer in interval notation.) Submit Skip (you cannot come back).2. [0.04/0.08 Points] PREVIOUS ANSWERS sasscucz 3.1.005. Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.) absolute maximum value 5 V absolute minimum value DNE v local maximum value(s) x local minimum value(s) X Need Help? 3. [fl/0.08 Points] PREVIOUS ANSWERS SESSCALCZ 3.1.010. ASK YOURTEACHER Sketch the graph offby hand and use your sketch to nd the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 2 cos t, 3:r/2 S t S 37r/2 absolute maximum I X absolute minimum X local maximum x local minimum X Sketch the graph offby hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(x)=2+(x+1)2, 3sx