What is the extreme f(x)=ln(1-x)+10x ?

The extreme f(x)=ln(1-x)+10x is Maximum(9/10 ,-ln(10)+9)

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extreme f(x)=ln(1-x)+10x

extreme

Maximum (\frac{9}{10}, - ln (10) + 9)

Solution steps

f^{'} (x) = - \frac{1}{1 - x} + 10

Find intervals:

Increasing

: - \infty < x < \frac{9}{10},

Decreasing

: \frac{9}{10} < x < 1

Plug

x = \frac{9}{10}

into

ln (1 - x) + 10 x : - ln (10) + 9

Maximum (\frac{9}{10}, - ln (10) + 9)

What is the extreme f(x)=ln(1-x)+10x ?
The extreme f(x)=ln(1-x)+10x is Maximum(9/10 ,-ln(10)+9)