Please answer the following questions

5. [-/3 Points] DETAILS MY NOTES SCALCLS1 4.2.021. ASK YOUR TEACHER PRACTICE ANOTHER Find the local maximum and minimum values of fusing both the First and Second Derivative Tests. (If an answer does not exist, enter DNE.) f ( x) = x+V7-x local maximum value local minimum value Which method do you prefer? First Derivative Test Second Derivative Test Submit Answer 6. [-/2 Points] DETAILS MY NOTES SCALCLS1 4.2.023.MI. ASK YOUR TEACHER PRACTICE ANOTHER Suppose f " is continuous on (-0o, co). (a) If f '(-5) = 0 and f "(-5) = -1, what can you say about f ? At x = -5, f has a local maximum. O At x = -5, f has a local minimum. At x = -5, fhas neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = -5. (b) If f '(-1) = 0 and f "(-1) = 0, what can you say about f ? O At x = -1, f has a local maximum. O At x = -1, f has a local minimum. At x = -1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = -1. Submit Answer 7. [-/7 Points] DETAILS MY NOTES SCALCLS1 4.2.026. ASK YOUR TEACHER PRACTICE ANOTHER Consider the function below. f(x) = 6+3x -x3 (a) Find the interval of increase. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval of decrease. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (b) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the inflection point. (If an answer does not exist, enter DNE.) ( x, y ) = ( Find the interval where the graph is concave upward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval where the graph is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Submit