What is the extreme (8x^2)/(x-6),-3<= x<= 2 ?

The extreme (8x^2)/(x-6),-3<= x<= 2 is Minimum(-3,-8),Maximum(0,0),Minimum(2,-8)

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extreme (8x^2)/(x-6),-3<= x<= 2

extreme points

\frac{8 x ^{2}}{x - 6}, - 3 \leq x \leq 2

Minimum (- 3, - 8), Maximum (0, 0), Minimum (2, - 8)

Solution steps

Find the critical points:

x = - 3, x = 0, x = 2

Domain of

\frac{8 x ^{2}}{x - 6}, - 3 \leq x \leq 2 : - 3 \leq x \leq 2

Find intervals:

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 2

Plug the extreme point

x = - 3

into

\frac{8 x ^{2}}{x - 6} \Rightarrow y = - 8

Minimum (- 3, - 8)

Plug the extreme point

x = 0

into

\frac{8 x ^{2}}{x - 6} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 2

into

\frac{8 x ^{2}}{x - 6} \Rightarrow y = - 8

Minimum (2, - 8)

Minimum (- 3, - 8), Maximum (0, 0), Minimum (2, - 8)

f (x, y) = x + 3 y

g (x) = x^{3} - 12 x^{2} + 45 x + 4

g (x) = x^{3} - 12 x^{2} + 45 x + 1

g (x) = x^{3} - 12 x^{2} + 45 x + 2

g (x) = x^{3} - 12 x^{2} + 45 x + 7

What is the extreme (8x^2)/(x-6),-3<= x<= 2 ?
The extreme (8x^2)/(x-6),-3<= x<= 2 is Minimum(-3,-8),Maximum(0,0),Minimum(2,-8)