4.3 Homework - Derivatives, Shape of a Graph (Homework)

1. [-/1 Points] DETAILS SCALCET9 4.3.005. MY NOTES ASK YOUR TEACHER The graph of the derivative f' of a function f is shown. y = f'(x) A (a) On what intervals is f increasing? (Enter your answer using interval notation.) On what intervals is f decreasing? (Enter your answer using interval notation.) (b) At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.) X =2. [-1'1 Points] SCALCETB 4.3.007. ASK YOUR TEACHER State the Xecoordinates of the inection points of the curve below. y (a) The curve is the graph of f. (Enter your answers as a commaiseparated list.) x: (h) The curve is the graph of 1". (Enter your answers as a Gamma-separated list.) (c) The curve is the graph of f". (Enter your answers as a comma-separated list.) Need Help? 3. [-/1 Points] DETAILS SCALCET9 4.3.020. MY NOTES ASK YOUR TEACHER Consider the following. (If an answer does not exist, enter DNE.) f(x) = In(2 + sin(x)), Oxs 2n Find the interval(s) on which f is concave up. (Enter your answer using interval notation.) Find the interval(s) on which fis concave down. (Enter your answer using interval notation.) Find the inflection points of f. smaller x-value ( x, y ) = larger x-value ( x, y ) = Need Help? Read It4. [-/1 Points] DETAILS SCALCET9 4.3.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. (If an answer does not exist, enter DNE.) f ( x ) = _ ex ex + 6 Find the interval(s) on which f is concave up. (Enter your answer using interval notation.) Find the interval(s) on which f is concave down. (Enter your answer using interval notation.) Find the inflection point of f. ( x, y ) = Need Help? Read It5. [-/1 Points] DETAILS SCALCET9 4.3.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the local maximum and local minimum values of fusing both the First and Second Derivative Tests. f(x) = 5+9x2 -6x3 local maximum value local minimum value Need Help? Read It