What is the extreme f(x)=-x^3+192ln(x) ?

The extreme f(x)=-x^3+192ln(x) is Maximum(4,-64+384ln(2))

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extreme f(x)=-x^3+192ln(x)

extreme points

f (x) = - x^{3} + 192 ln (x)

Maximum (4, - 64 + 384 ln (2))

Solution steps

f^{'} (x) = - 3 x^{2} + \frac{192}{x}

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 4

into

- x^{3} + 192 ln (x) : - 64 + 384 ln (2)

Maximum (4, - 64 + 384 ln (2))

What is the extreme f(x)=-x^3+192ln(x) ?
The extreme f(x)=-x^3+192ln(x) is Maximum(4,-64+384ln(2))