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

6. [-/1 Points] DETAILS SCALCET9 4.3.043. MY NOTES ASK YOUR TEACHER The graph of the derivative f' of a continuous function f is shown. (Assume f' continues to co.) -4 y = f'( x ) 2 6 8 -2 A (a) On what interval(s) is f increasing? (Enter your answer in interval notation.) On what interval(s) is f decreasing? (Enter your answer in interval notation.) (b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) X = At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) X = (c) On what interval(s) is f concave upward? (Enter your answer in interval notation.) On what interval(s) is f concave downward? (Enter your answer in interval notation.)(d) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.) X = (e) Assuming that f(0) = 0, sketch a graph of f. 2 4 X 6 8 -1 2 4 6 X 8 -2 -2 - 3 - 3 3 -4 -4 2 -5 -5 -6 - 6 X 2 4 X 6 8 @0-7 Need Help? Read It Watch It Submit Answer7. [-/1 Points] DETAILS SCALCET9 4.3.053. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. (If an answer does not exist, enter DNE.) F(x) = xV6-x (a) Find the interval(s) of increase. (Enter your answer using interval notation.) Find the interval(s) of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection point. ( x, y ) = ( Find the interval(s) where the function is concave up. (Enter your answer using interval notation.) Find the interval(s) where the function is concave down. (Enter your answer using interval notation.)(d) Use the information from parts (ark) to sketch the graph. Check your work with a graphing calculator of computer. y Need Help? 8. [-/1 Points] DETAILS SCALCET9 4.3.061. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following function. (If an answer does not exist, enter DNE.) f ( x ) = e-2/x (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) X = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.) y : (b) Find the interval(s) of increase. (Enter your answer using interval notation.) Find the interval(s) of decrease. (Enter your answer using interval notation.) (c) Find the local maximum and minimum values. local maximum value local minimum value (d) Find the interval(s) on which fis 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 point. ( x, V ) =(e) Use the information from parts (a)-(d) to sketch the graph of f. 1.4 41 1.2- 31 ---1:0- 0.8 21 0.6- --1 0.4 0.2 O-40 -20 X 20 40 10-40 -20 20 40 10-40 -20 20 40 A 0-40 -20 20 40 A Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 4.3.095. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the inflection point of the function. (Hint: g"(0) does not exist.) g(x) = 7xx| (x, g(x) ) = ( Need Help? Read It Watch It 10. [-/1 Points] DETAILS SCALCET8 4.3.JIT.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Factor the expression completely. x3 + 14x2 + 49x Need Help? Watch It