What is the extreme f(x)=3-x,1<= x<= 3 ?

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

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extreme f(x)=3-x,1<= x<= 3

extreme points

f (x) = 3 - x, 1 \leq x \leq 3

Maximum (1, 2), Minimum (3, 0)

Solution steps

Find the critical points:

x = 1, x = 3

Domain of

3 - x, 1 \leq x \leq 3 : 1 \leq x \leq 3

Find intervals:

Decreasing

: 1 < x < 3

Plug the extreme point

x = 1

into

3 - x \Rightarrow y = 2

Maximum (1, 2)

Plug the extreme point

x = 3

into

3 - x \Rightarrow y = 0

Minimum (3, 0)

Maximum (1, 2), Minimum (3, 0)

f (x) = x^{3} e^{(4 - 2 x^{2})}

x^{2} - x y + y^{2} + 9 x - 6 y + 10

f (x) = 39 x^{\frac{27}{13}} - 81 x

x y^{2} + x^{3} y - x y

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