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Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.)f(x) = x2 − 6x − 2,    [0, 3]absolute maximum    (x, y) =        absolute minimum    (x, y) =

Question

Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.)

f(x) = x2 − 6x − 2,    [0, 3]
absolute maximum     (x, y)  = 
 
 
 
 
 
 
 
absolute minimum     (x, y)  = 
 
 
 
 
 
 
check_circleAnswer
Step 1

To find absolute extrema, take derivative and check the intervals using f(x). Apply power rule to take derivative

- x* - 6х -2
-бх — 2
f(x)
(x)'n
т
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- x* - 6х -2 -бх — 2 f(x) (x)'n т

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Step 2

Apply power rule to find derivative. Set derivative =0 and solve for x

f'(x) 2x-6
0 2x-6
6 2x
3 x
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f'(x) 2x-6 0 2x-6 6 2x 3 x

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Step 3

Critical value is x=3, Given interval is [...

f(x)x6x2
f(0)= 02 -6(0)-2 =-2
f(3) (3) -6(3)-2 = -11
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f(x)x6x2 f(0)= 02 -6(0)-2 =-2 f(3) (3) -6(3)-2 = -11

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Tagged in

Math

Calculus

Derivative

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