What is the extreme f(x)=x^2-6x,-1<= x<= 6 ?

The extreme f(x)=x^2-6x,-1<= x<= 6 is Maximum(-1,7),Minimum(3,-9),Maximum(6,0)

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extreme f(x)=x^2-6x,-1<= x<= 6

extreme points

f (x) = x^{2} - 6 x, - 1 \leq x \leq 6

Maximum (- 1, 7), Minimum (3, - 9), Maximum (6, 0)

Solution steps

Find the critical points:

x = - 1, x = 3, x = 6

Domain of

x^{2} - 6 x, - 1 \leq x \leq 6 : - 1 \leq x \leq 6

Find intervals:

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < 6

Plug the extreme point

x = - 1

into

x^{2} - 6 x \Rightarrow y = 7

Maximum (- 1, 7)

Plug the extreme point

x = 3

into

x^{2} - 6 x \Rightarrow y = - 9

Minimum (3, - 9)

Plug the extreme point

x = 6

into

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

Maximum (6, 0)

Maximum (- 1, 7), Minimum (3, - 9), Maximum (6, 0)

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

\frac{4 x - 12}{( x - 2 ) ^{2}}

f (x) = 3 x^{3} - 3 x^{2} - 3 x + 2, - 1 \leq x \leq 0

f (x, y) = x^{2} + y^{2} - 4 x + 17 x - 10 y + 2021

f (x) = 18 x^{2} - 32 y^{2} - 36 x - 128 y - 110

What is the extreme f(x)=x^2-6x,-1<= x<= 6 ?
The extreme f(x)=x^2-6x,-1<= x<= 6 is Maximum(-1,7),Minimum(3,-9),Maximum(6,0)