What is the extreme f(x)=x^3+2x^2-20x,0<= x<= 3 ?

The extreme f(x)=x^3+2x^2-20x,0<= x<= 3 is Maximum(0,0),Minimum(2,-24),Maximum(3,-15)

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extreme f(x)=x^3+2x^2-20x,0<= x<= 3

extreme points

f (x) = x^{3} + 2 x^{2} - 20 x, 0 \leq x \leq 3

Maximum (0, 0), Minimum (2, - 24), Maximum (3, - 15)

Solution steps

Find the critical points:

x = 0, x = 2, x = 3

Domain of

x^{3} + 2 x^{2} - 20 x, 0 \leq x \leq 3 : 0 \leq x \leq 3

Find intervals:

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < 3

Plug the extreme point

x = 0

into

x^{3} + 2 x^{2} - 20 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 2

into

x^{3} + 2 x^{2} - 20 x \Rightarrow y = - 24

Minimum (2, - 24)

Plug the extreme point

x = 3

into

x^{3} + 2 x^{2} - 20 x \Rightarrow y = - 15

Maximum (3, - 15)

Maximum (0, 0), Minimum (2, - 24), Maximum (3, - 15)

x^{\frac{13}{3}} - 9 x^{\frac{7}{3}}

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

x^{3} - 9 x + 2

f (x) = 2 x^{3} - 9 x^{2} - 60 x + 8

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

What is the extreme f(x)=x^3+2x^2-20x,0<= x<= 3 ?
The extreme f(x)=x^3+2x^2-20x,0<= x<= 3 is Maximum(0,0),Minimum(2,-24),Maximum(3,-15)