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

The extreme f(x)=x^2,-1<= x<= 2 is Maximum(-1,1),Minimum(0,0),Maximum(2,4)

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

extreme points

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

Maximum (- 1, 1), Minimum (0, 0), Maximum (2, 4)

Solution steps

Find the critical points:

x = - 1, x = 0, x = 2

Domain of

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

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 2

Plug the extreme point

x = - 1

into

x^{2} \Rightarrow y = 1

Maximum (- 1, 1)

Plug the extreme point

x = 0

into

x^{2} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 2

into

x^{2} \Rightarrow y = 4

Maximum (2, 4)

Maximum (- 1, 1), Minimum (0, 0), Maximum (2, 4)

f (x) = 3 y^{2} + 8 y

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

f (x) = \frac{1}{2} x - sin (x)

f (x) = 2 x^{2} + 3 x + 2

f (x) = x e^{3 - (\frac{x}{4})}

What is the extreme f(x)=x^2,-1<= x<= 2 ?
The extreme f(x)=x^2,-1<= x<= 2 is Maximum(-1,1),Minimum(0,0),Maximum(2,4)