What is the extreme f(x)=x-6sqrt(x-1) ?

The extreme f(x)=x-6sqrt(x-1) is Minimum(1,1),Minimum(10,-8)

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extreme f(x)=x-6sqrt(x-1)

extreme points

f (x) = x - 6 x - 1

Minimum (1, 1), Minimum (10, - 8)

Solution steps

f^{'} (x) = 1 - \frac{3}{x - 1}

Find intervals:

Increasing

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

Decreasing

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

Plug

x = 1

into

x - 6 x - 1 : 1

Minimum (1, 1)

Plug

x = 10

into

x - 6 x - 1 : - 8

Minimum (10, - 8)

Minimum (1, 1), Minimum (10, - 8)

f (x, y) = x^{3} + y^{3} - 15 x y

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

f (x) = 2 x + 1 - \frac{18}{x}

f (x, y) = y - x

f (x, y) = 100 - x^{2} - y^{2}

What is the extreme f(x)=x-6sqrt(x-1) ?
The extreme f(x)=x-6sqrt(x-1) is Minimum(1,1),Minimum(10,-8)