What is the extreme f(x)=(16x-20)*ln(4x-5) ?

The extreme f(x)=(16x-20)*ln(4x-5) is Minimum((1+5e}{4e}, 4/e ln(\frac{1+5e)/e-5))

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extreme f(x)=(16x-20)*ln(4x-5)

extreme points

f (x) = (16 x - 20) \cdot ln (4 x - 5)

Minimum (\frac{1 + 5 e}{4 e}, \frac{4}{e} ln (\frac{1 + 5 e}{e} - 5))

Solution steps

f^{'} (x) = 16 (ln (4 x - 5) + 1)

Find intervals:

Decreasing

: \frac{5}{4} < x < \frac{1 + 5 e}{4 e},

Increasing

: \frac{1 + 5 e}{4 e} < x < \infty

Plug

x = \frac{1 + 5 e}{4 e}

into

(16 x - 20) \cdot ln (4 x - 5) : \frac{4}{e} ln (\frac{1 + 5 e}{e} - 5)

Minimum (\frac{1 + 5 e}{4 e}, \frac{4}{e} ln (\frac{1 + 5 e}{e} - 5))

f (x) = 3 x^{4} - 6 x^{3} + 9

2300 x - 2 x^{2}

f (x) = x^{2} + x y + y^{2} - 34 y + 385

f (x) = (x^{2} - 4)^{3}, (- 2, 3)

f (x) = x^{3} - \frac{3}{2} x^{2}, - 5 \leq x \leq 4

What is the extreme f(x)=(16x-20)*ln(4x-5) ?
The extreme f(x)=(16x-20)*ln(4x-5) is Minimum((1+5e}{4e}, 4/e ln(\frac{1+5e)/e-5))