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Popular Functions >

extreme f(x)=2x-11ln(8x),2<= x<= 9

Solution

extreme

Solution

Maximum (2, 4 - 44 ln (2)), Minimum (\frac{11}{2}, 11 - 11 ln (44)), Maximum (9, 18 - 11 ln (72))

Solution steps

Find the critical points:

x = 2, x = \frac{11}{2}, x = 9

Domain of

2 x - 11 ln (8 x), 2 \leq x \leq 9 : 2 \leq x \leq 9

Find intervals:

Decreasing

: 2 < x < \frac{11}{2},

Increasing

: \frac{11}{2} < x < 9

Plug the extreme point

x = 2

into

2 x - 11 ln (8 x) \Rightarrow y = 4 - 44 ln (2)

Maximum (2, 4 - 44 ln (2))

Plug the extreme point

x = \frac{11}{2}

into

2 x - 11 ln (8 x) \Rightarrow y = 11 - 11 ln (44)

Minimum (\frac{11}{2}, 11 - 11 ln (44))

Plug the extreme point

x = 9

into

2 x - 11 ln (8 x) \Rightarrow y = 18 - 11 ln (72)

Maximum (9, 18 - 11 ln (72))

Maximum (2, 4 - 44 ln (2)), Minimum (\frac{11}{2}, 11 - 11 ln (44)), Maximum (9, 18 - 11 ln (72))

Graph

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