What is the extreme f(x)=x^{1/3}(x-4),-125<= x<= 125 ?

The extreme f(x)=x^{1/3}(x-4),-125<= x<= 125 is Maximum(-125,645),Minimum(1,-3),Maximum(125,605)

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extreme f(x)=x^{1/3}(x-4),-125<= x<= 125

extreme points

f (x) = x^{\frac{1}{3}} (x - 4), - 125 \leq x \leq 125

Maximum (- 125, 645), Minimum (1, - 3), Maximum (125, 605)

Solution steps

Find the critical points:

x = - 125, x = 0, x = 1, x = 125

Domain of

x^{\frac{1}{3}} (x - 4), - 125 \leq x \leq 125 : - 125 \leq x \leq 125

Find intervals:

Decreasing

: - 125 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 125

Plug the extreme point

x = - 125

into

x^{\frac{1}{3}} (x - 4) \Rightarrow y = 645

Maximum (- 125, 645)

Plug the extreme point

x = 1

into

x^{\frac{1}{3}} (x - 4) \Rightarrow y = - 3

Minimum (1, - 3)

Plug the extreme point

x = 125

into

x^{\frac{1}{3}} (x - 4) \Rightarrow y = 605

Maximum (125, 605)

Maximum (- 125, 645), Minimum (1, - 3), Maximum (125, 605)

x (16 - 2 x)

f (x) = \frac{ln ( x )}{x} + 1

f (x) = \frac{2 x ^{2} + 8}{x}

f (x) = 9 x^{3} - 2 7^{2} + 5 x + 42

f (x) = x^{3} - 2 x^{2} - 15 x + 5 (2.2)

What is the extreme f(x)=x^{1/3}(x-4),-125<= x<= 125 ?
The extreme f(x)=x^{1/3}(x-4),-125<= x<= 125 is Maximum(-125,645),Minimum(1,-3),Maximum(125,605)