What is the extreme f(x)=3x^2-x^3,1<= x<= 5 ?

The extreme f(x)=3x^2-x^3,1<= x<= 5 is Minimum(1,2),Maximum(2,4),Minimum(5,-50)

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extreme f(x)=3x^2-x^3,1<= x<= 5

extreme points

f (x) = 3 x^{2} - x^{3}, 1 \leq x \leq 5

Minimum (1, 2), Maximum (2, 4), Minimum (5, - 50)

Solution steps

Find the critical points:

x = 1, x = 2, x = 5

Domain of

3 x^{2} - x^{3}, 1 \leq x \leq 5 : 1 \leq x \leq 5

Find intervals:

Increasing

: 1 < x < 2,

Decreasing

: 2 < x < 5

Plug the extreme point

x = 1

into

3 x^{2} - x^{3} \Rightarrow y = 2

Minimum (1, 2)

Plug the extreme point

x = 2

into

3 x^{2} - x^{3} \Rightarrow y = 4

Maximum (2, 4)

Plug the extreme point

x = 5

into

3 x^{2} - x^{3} \Rightarrow y = - 50

Minimum (5, - 50)

Minimum (1, 2), Maximum (2, 4), Minimum (5, - 50)

f (x, y) = x^{2} + y^{3} - 4 x - 3 y

f (x) = cos (3 x) - 2

f (x) = - sin (x) - 4

f (x) = 2 x^{3} - x^{2} - 4 x + 8 (- 1)

f (x, y) = 2 x^{5} + x^{3} y^{2} + 6 x y^{4}

What is the extreme f(x)=3x^2-x^3,1<= x<= 5 ?
The extreme f(x)=3x^2-x^3,1<= x<= 5 is Minimum(1,2),Maximum(2,4),Minimum(5,-50)