Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema33x2 - 4x +52f(x)Select the correct choice below and, if necessary, fill in any answer boxes within your choiceO A. The function has a relative maximum ofat xand a relative minimum ofat x(Use a comma to separate answers as needed.)B. There are no relative minima. The function has a relative maximum ofat x(Use a comma to separate answers as needed.)O C. There are no relative maxima. The function has a relative minimum ofat x(Use a comma to separate answers as needed.)D. There are no relative extrema.

Question
Asked Oct 22, 2019
Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema
33
x2 - 4x +5
2
f(x)
Select the correct choice below and, if necessary, fill in any answer boxes within your choice
O A. The function has a relative maximum of
at x
and a relative minimum of
at x
(Use a comma to separate answers as needed.)
B. There are no relative minima. The function has a relative maximum of
at x
(Use a comma to separate answers as needed.)
O C. There are no relative maxima. The function has a relative minimum of
at x
(Use a comma to separate answers as needed.)
D. There are no relative extrema.
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Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema 33 x2 - 4x +5 2 f(x) Select the correct choice below and, if necessary, fill in any answer boxes within your choice O A. The function has a relative maximum of at x and a relative minimum of at x (Use a comma to separate answers as needed.) B. There are no relative minima. The function has a relative maximum of at x (Use a comma to separate answers as needed.) O C. There are no relative maxima. The function has a relative minimum of at x (Use a comma to separate answers as needed.) D. There are no relative extrema.

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Expert Answer

Step 1

Given,

8
x
33
x2 - 4x5
f(x)
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8 x 33 x2 - 4x5 f(x)

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Step 2

Now, differentiating with respect to x, we get

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Step 3

A relative maximum point is a point where the function changes direction from increasing to decreasing.

Similarly, ...

Sign of f'(x)
f'(x)
Interval
(00,-4)
0
-4
8
1
< 0
So, -4 is the point of relative minima and --- is the point of relative maxima.
f(-4) -4)3(-4)4-4)
8
217
( -(-
f ()
8
33
2015
4
2.
384
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Sign of f'(x) f'(x) Interval (00,-4) 0 -4 8 1 < 0 So, -4 is the point of relative minima and --- is the point of relative maxima. f(-4) -4)3(-4)4-4) 8 217 ( -(- f () 8 33 2015 4 2. 384

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Math

Calculus

Derivative