What is the extreme f(x)=x^3+3x^2-24x,-1<= x<= 3 ?

The extreme f(x)=x^3+3x^2-24x,-1<= x<= 3 is Maximum(-1,26),Minimum(2,-28),Maximum(3,-18)

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extreme f(x)=x^3+3x^2-24x,-1<= x<= 3

extreme points

f (x) = x^{3} + 3 x^{2} - 24 x, - 1 \leq x \leq 3

Maximum (- 1, 26), Minimum (2, - 28), Maximum (3, - 18)

Solution steps

Find the critical points:

x = - 1, x = 2, x = 3

Domain of

x^{3} + 3 x^{2} - 24 x, - 1 \leq x \leq 3 : - 1 \leq x \leq 3

Find intervals:

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < 3

Plug the extreme point

x = - 1

into

x^{3} + 3 x^{2} - 24 x \Rightarrow y = 26

Maximum (- 1, 26)

Plug the extreme point

x = 2

into

x^{3} + 3 x^{2} - 24 x \Rightarrow y = - 28

Minimum (2, - 28)

Plug the extreme point

x = 3

into

x^{3} + 3 x^{2} - 24 x \Rightarrow y = - 18

Maximum (3, - 18)

Maximum (- 1, 26), Minimum (2, - 28), Maximum (3, - 18)

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

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

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

f (x) = 3 x^{3} - x

f (x) = 6 x e^{- 0.6 x}

What is the extreme f(x)=x^3+3x^2-24x,-1<= x<= 3 ?
The extreme f(x)=x^3+3x^2-24x,-1<= x<= 3 is Maximum(-1,26),Minimum(2,-28),Maximum(3,-18)