What is the extreme x^3-3/2 x^2,-1<= x<= 4 ?

The extreme x^3-3/2 x^2,-1<= x<= 4 is Minimum(-1,-5/2),Maximum(0,0),Minimum(1,-1/2),Maximum(4,40)

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extreme x^3-3/2 x^2,-1<= x<= 4

extreme

Minimum (- 1, - \frac{5}{2}), Maximum (0, 0), Minimum (1, - \frac{1}{2}), Maximum (4, 40)

Solution steps

Find the critical points:

x = - 1, x = 0, x = 1, x = 4

Domain of

x^{3} - \frac{3}{2} x^{2}, - 1 \leq x \leq 4 : - 1 \leq x \leq 4

Find intervals:

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 4

Plug the extreme point

x = - 1

into

x^{3} - \frac{3}{2} x^{2} \Rightarrow y = - \frac{5}{2}

Minimum (- 1, - \frac{5}{2})

Plug the extreme point

x = 0

into

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

Maximum (0, 0)

Plug the extreme point

x = 1

into

x^{3} - \frac{3}{2} x^{2} \Rightarrow y = - \frac{1}{2}

Minimum (1, - \frac{1}{2})

Plug the extreme point

x = 4

into

x^{3} - \frac{3}{2} x^{2} \Rightarrow y = 40

Maximum (4, 40)

Minimum (- 1, - \frac{5}{2}), Maximum (0, 0), Minimum (1, - \frac{1}{2}), Maximum (4, 40)

What is the extreme x^3-3/2 x^2,-1<= x<= 4 ?
The extreme x^3-3/2 x^2,-1<= x<= 4 is Minimum(-1,-5/2),Maximum(0,0),Minimum(1,-1/2),Maximum(4,40)