Suppose the function f(x) has a domain of all real numbers except x = 3 . The first derivative of f(x) is shown below.

Question

f '(x) = 5(x − 1)e^8x/(x − 3)^5

a. Find the interval(s) where f(x) is increasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

b. Find the interval(s) where f(x) is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

c. Find the x-coordinates of all local extrema on the graph of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Local Maxima at x = 

Local Minima at x =

Answer 1

Use interval identification techniques presented in Algebra 2.