ind the x-values of all points where the function has any relative extrema. Find
ID: 2885557 • Letter: I
Question
ind the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema f(x)=2-3x2-24x-2 Select the correct choice below and, if necessary, ill in any answer boxes within your choice. There are no relative maxima. The function has a relative minimum of? atx-O A (Use a comma to separate answers as needed) (Use a comma to separate answers as needed) (Use a comma to separate answers as needed.) B. The function has a relative maximum of?atxz[ and a relative minimum of atx1 ° C. There are no relative minima The function has a relative maximum of ? at x- 0 D. There are no relative extrema.Explanation / Answer
f(x) = x3-3x2-24x-2
f '(x) = 3x2-6x-24
Critical numbers , f'(x)=0
3(x2-2x-8)=0
x2-2x-8=0
(x-4)(x+2)=0
x =-2 , 4
At x=-2, sign of f'(x) change from positive to negative. So there is relative maximum at x=-2 which is 26
At x=4 , sign of f'(x) change from negative to positive. So there is relative minimum at x=4 which is -82.
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