10. -1.81 points 0 My Notes For the function defined below, determine each of th
ID: 2889558 • Letter: 1
Question
10. -1.81 points 0 My Notes For the function defined below, determine each of the following. (x)--3(x2-36x + 180 (a) Find the critical values of fx). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (b) Find the intervals on which rx) is increasing and the intervals on which is decreasing. Enter your answer using interval notation. Decreasing (c) Find the x-coordinates of all relative extrema on the graph of x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Relative Maxima: Relative Minima:Explanation / Answer
a)
f(x) = -3(x²-36x+180)^(2/3)
Find derivative as
f'(x) = -3*(2/3) *(x²-36x+180)^(2/3 -1) *(2x-36)
= -4(x-18)/(x²-36x+180)^(1/3)
Functin has critical point when f'(x) = 0 or f'(x) is undefined. hence
x-18 = 0 gives x =18
x² -36x +180 = 0 gives (x-6) (x-30) = 0 gives x =6, 30
Thus, critical points are
x=6, 18, 30
==========
b)
Increasing in interval (-,6)U(18,30)
decreasing in interval (6,18)U(30,)
c)
Relative maxima at 6,30
Relative minima at 18
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