What is the extreme f(x)=x^2-11,-2<= x<= 4 ?

The extreme f(x)=x^2-11,-2<= x<= 4 is Maximum(-2,-7),Minimum(0,-11),Maximum(4,5)

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extreme f(x)=x^2-11,-2<= x<= 4

extreme points

f (x) = x^{2} - 11, - 2 \leq x \leq 4

Maximum (- 2, - 7), Minimum (0, - 11), Maximum (4, 5)

Solution steps

Find the critical points:

x = - 2, x = 0, x = 4

Domain of

x^{2} - 11, - 2 \leq x \leq 4 : - 2 \leq x \leq 4

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 4

Plug the extreme point

x = - 2

into

x^{2} - 11 \Rightarrow y = - 7

Maximum (- 2, - 7)

Plug the extreme point

x = 0

into

x^{2} - 11 \Rightarrow y = - 11

Minimum (0, - 11)

Plug the extreme point

x = 4

into

x^{2} - 11 \Rightarrow y = 5

Maximum (4, 5)

Maximum (- 2, - 7), Minimum (0, - 11), Maximum (4, 5)

f (x) = 3 x^{3} - 36 x^{2} + 108 x + 8

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

f (x) = \frac{x}{2} - sin (x), - π \leq x \leq π

y = x^{2} (x - 3)

f (x) = x (20 - 2 x) (12 - 2 x)

What is the extreme f(x)=x^2-11,-2<= x<= 4 ?
The extreme f(x)=x^2-11,-2<= x<= 4 is Maximum(-2,-7),Minimum(0,-11),Maximum(4,5)