What is the extreme f(x)= 1/4 x-ln(x) ?

The extreme f(x)= 1/4 x-ln(x) is Minimum(4,1-2ln(2))

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extreme f(x)= 1/4 x-ln(x)

extreme points

f (x) = \frac{1}{4} x - ln (x)

Minimum (4, 1 - 2 ln (2))

Solution steps

f^{'} (x) = \frac{1}{4} - \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 4

into

\frac{1}{4} x - ln (x) : 1 - 2 ln (2)

Minimum (4, 1 - 2 ln (2))

f (x) = 4 - 4 x^{2}

y = x^{3} - 2 x + 4

f (x) = x^{2} + x y + y^{2} - 13 y + 56

f (x) = 5 x^{3} - 5 x^{2} - 5 x + 8, - 1 \leq x \leq 2

f (x) = (3 - x) 3^{x}

What is the extreme f(x)= 1/4 x-ln(x) ?
The extreme f(x)= 1/4 x-ln(x) is Minimum(4,1-2ln(2))