What is the extreme f(x)=-x^2+50ln(x) ?

The extreme f(x)=-x^2+50ln(x) is Maximum(5,-25+50ln(5))

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extreme f(x)=-x^2+50ln(x)

extreme points

f (x) = - x^{2} + 50 ln (x)

Maximum (5, - 25 + 50 ln (5))

Solution steps

f^{'} (x) = - 2 x + \frac{50}{x}

Find intervals:

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 5

into

- x^{2} + 50 ln (x) : - 25 + 50 ln (5)

Maximum (5, - 25 + 50 ln (5))

f (x) = - 69.7 x^{2} + 625.6 x

f (x) = \frac{1}{2} (x + 4)^{2} + 6

f (x) = - 0.3 x^{2} + 2.4 x + 98.8

\frac{2}{x + 3} - 1

f (x, y) = x y + e^{x y}

What is the extreme f(x)=-x^2+50ln(x) ?
The extreme f(x)=-x^2+50ln(x) is Maximum(5,-25+50ln(5))