What is the extreme f(x)=x+log_{10}(1-x) ?

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

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extreme f(x)=x+log_{10}(1-x)

extreme

Maximum (- \frac{1}{ln ( 10 )} + 1, - \frac{1}{ln ( 10 )} + 1 + lo g_{10} (\frac{1}{ln ( 10 )}))

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{ln ( 10 )} + 1,

Decreasing

: - \frac{1}{ln ( 10 )} + 1 < x < 1

Plug

x = - \frac{1}{ln ( 10 )} + 1

into

x + lo g_{10} (1 - x) : - \frac{1}{ln ( 10 )} + 1 + lo g_{10} (\frac{1}{ln ( 10 )})

Maximum (- \frac{1}{ln ( 10 )} + 1, - \frac{1}{ln ( 10 )} + 1 + lo g_{10} (\frac{1}{ln ( 10 )}))

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