For the function defined below, determine each of the following. f(x) = 3 x2 16x

Question

For the function defined below, determine each of the following. f(x) = 3 x2 16x + 60 2/3 (a) Find the critical values of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x = (b) Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Enter your answer using interval notation. Increasing: Decreasing: (c) 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:

Explanation / Answer

given f(x) = 3x2 16x +60

f '(x)=6x -16

for critical points f '(x)=0

=>6x-16=0

=>x=8/3

b)f(x) is increasing when f '(x)>0

=>6x-16>0

=>x>8/3

x =(8/3,infinity)

f(x) is decreasing when f '(x)<0

=>6x-16<0

=>x<8/3

x =(-infinity,8/3)

c)at x =8/3, f '(x) changes its sign from negative to positive

=>relative minima at x =8/3

relative maxima DNE

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