What is the extreme f(x)=x^2-11,-2<= x<= 3 ?

The extreme f(x)=x^2-11,-2<= x<= 3 is Maximum(-2,-7),Minimum(0,-11),Maximum(3,-2)

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extreme f(x)=x^2-11,-2<= x<= 3

extreme points

f (x) = x^{2} - 11, - 2 \leq x \leq 3

Maximum (- 2, - 7), Minimum (0, - 11), Maximum (3, - 2)

Solution steps

Find the critical points:

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

Domain of

x^{2} - 11, - 2 \leq x \leq 3 : - 2 \leq x \leq 3

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 3

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 = 3

into

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

Maximum (3, - 2)

Maximum (- 2, - 7), Minimum (0, - 11), Maximum (3, - 2)

f (x y) = x^{3} + y^{2} - 6 x y + 9 x + 5 y + 2

f (x, y) = e^{- x - y^{2}} \cdot (3 x - y^{2})

x^{2} + y^{2} + 2 x - 4 y + 8

f (x) = \frac{( 3 x - 6 )}{( x + 2 )}

f (x, y) = 3 x^{3} - y^{3} - 9 x + 12 y + 3

What is the extreme f(x)=x^2-11,-2<= x<= 3 ?
The extreme f(x)=x^2-11,-2<= x<= 3 is Maximum(-2,-7),Minimum(0,-11),Maximum(3,-2)