What is the extreme f(x)=-5x^6ln(x),(0,4) ?

The extreme f(x)=-5x^6ln(x),(0,4) is Maximum(1/(\sqrt[6]{e)}, 5/(6e))

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extreme f(x)=-5x^6ln(x),(0,4)

extreme points

f (x) = - 5 x^{6} ln (x), (0, 4)

Maximum (\frac{1}{6 e}, \frac{5}{6 e})

Solution steps

Find the critical points:

x = \frac{1}{6 e}

Domain of

- 5 x^{6} ln (x), (0, 4) : 0 < x < 4

Find intervals:

Increasing

: 0 < x < \frac{1}{6 e},

Decreasing

: \frac{1}{6 e} < x < 4

Plug the extreme point

x = \frac{1}{6 e}

into

- 5 x^{6} ln (x) \Rightarrow y = \frac{5}{6 e}

Maximum (\frac{1}{6 e}, \frac{5}{6 e})

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f (x) = 5 x + 5 sin (x), 0 \leq x \leq 2 π

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

f (x) = \frac{x ^{2}}{x ^{2} + 27}

f (x) = 2 x^{2} + 4 x + 10

What is the extreme f(x)=-5x^6ln(x),(0,4) ?
The extreme f(x)=-5x^6ln(x),(0,4) is Maximum(1/(\sqrt[6]{e)}, 5/(6e))