What is the extreme f(x)= x/(x-2),4<= x<= 6 ?

The extreme f(x)= x/(x-2),4<= x<= 6 is Maximum(4,2),Minimum(6, 3/2)

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extreme f(x)= x/(x-2),4<= x<= 6

extreme points

f (x) = \frac{x}{x - 2}, 4 \leq x \leq 6

Maximum (4, 2), Minimum (6, \frac{3}{2})

Solution steps

Find the critical points:

x = 4, x = 6

Domain of

\frac{x}{x - 2}, 4 \leq x \leq 6 : 4 \leq x \leq 6

Find intervals:

Decreasing

: 4 < x < 6

Plug the extreme point

x = 4

into

\frac{x}{x - 2} \Rightarrow y = 2

Maximum (4, 2)

Plug the extreme point

x = 6

into

\frac{x}{x - 2} \Rightarrow y = \frac{3}{2}

Minimum (6, \frac{3}{2})

Maximum (4, 2), Minimum (6, \frac{3}{2})

\frac{x}{x ^{2} - 16}

f (x) = 4 sin (2 x)

f (x) = \frac{( 2 x ^{2} + x - 3 )}{( 3 x - 9 )}

f (x, y) = x^{2} - y^{2} - 20 x + 2 y + 8

f (x, y) = \frac{x y}{x ^{2} + 1}

What is the extreme f(x)= x/(x-2),4<= x<= 6 ?
The extreme f(x)= x/(x-2),4<= x<= 6 is Maximum(4,2),Minimum(6, 3/2)