4. 1.81 points For the function below, determine each of the following 9 x824x-1

Question

4. 1.81 points For the function below, determine each of the following 9 x824x-17 (a) Find the critical values of g(x). (Enter your answers as a comma-separated list.) (b) Find the intervals on which gtx) is increasing and the intervals on which gx) is decreasing. Enter your answers using interval notation. Increasing Decreasing (c) Find the x-coordinates of all relative extrema on the graph of g(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Relative Maxima: Relative Minima

Explanation / Answer

given g(x) = 3x8 + 24x7- 17

g'(x) = d/dx [ 3x8 + 24x7- 17 ]

= 24x7+24*7 x6

for critical points g'(x) = 0

  24x7+24*7 x6 = 0

24x6(x + 7) =0

x=0 and x= - 7

a. critical points are x=-7 , 0

b. g(x) increase for (-7, infinity)

decrease for (-infinity , -7 )

c. relative minima ( - 7, -2470646 )

maxima ( 0, -17)

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