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C Secure https://www.webassign.net/web/Student/Assignment-Responses/last?dep-18036262 8. 11.81 points 0/6 Submissions Used Suppose the function f(x) has a domain of all real numbers except x-6. The first derivative of f(x) is shown below. -5x-3) (x 6)5 f(x) Find the intervals where f(x) is increasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Find the intervals where f(x) is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Find the x-coordinates of all relative extrema on the graph of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Relative Maxima: Relative Minima: image2.jpeg s image1 (1).jpeg e screen-shot-2012-0 webp Show A a image3.jpegExplanation / Answer
f(x) is increasing when f'(x) > 0
5(x-3)/(x+6)^5 >0
when x< -6 or x >3
hence increasing in interval (-, -6)U(3,)
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hence decreasing in interval (-6,3)
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Find derivative of f'(x) =5(x-3)/(x+6)^5 as
f"(x) = -5(4x-21)/(x+6)^6
now
f"(3) = 5/59049 >0 which means at x= 3 function has minima.
Relative maxima :DNE
Relative minima : 3
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