What is the extreme f(x)=-5x^7ln(2x),(0,6) ?

The extreme f(x)=-5x^7ln(2x),(0,6) is Maximum(1/(2\sqrt[7]{e)}, 5/(896e))

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extreme f(x)=-5x^7ln(2x),(0,6)

extreme points

f (x) = - 5 x^{7} ln (2 x), (0, 6)

Solution steps

Find the critical points:

Domain of

- 5 x^{7} ln (2 x), (0, 6) : 0 < x < 6

Find intervals:

Increasing

Decreasing

Plug the extreme point

into

- 5 x^{7} ln (2 x) \Rightarrow y = \frac{5}{896 e}

- x^{3} + 12 x

f (x) = - \frac{1}{3} x^{3} + \frac{1}{2} x^{2} + 2 x - \frac{1}{3}

y = x^{2} - 12 x + 1

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}}

(x - 2)^{3}

What is the extreme f(x)=-5x^7ln(2x),(0,6) ?
The extreme f(x)=-5x^7ln(2x),(0,6) is Maximum(1/(2\sqrt[7]{e)}, 5/(896e))