What is the extreme f(x)=4(x^{(10/3)})-10(x^{(4/3)}) ?

The extreme f(x)=4(x^{(10/3)})-10(x^{(4/3)}) is Minimum(-1,-6),Maximum(0,0),Minimum(1,-6)

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extreme f(x)=4(x^{(10/3)})-10(x^{(4/3)})

extreme points

f (x) = 4 (x^{(\frac{10}{3})}) - 10 (x^{(\frac{4}{3})})

Minimum (- 1, - 6), Maximum (0, 0), Minimum (1, - 6)

Solution steps

Find the critical points:

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

Domain of

4 x^{\frac{10}{3}} - 10 x^{\frac{4}{3}} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = - 1

into

4 x^{\frac{10}{3}} - 10 x^{\frac{4}{3}} \Rightarrow y = - 6

Minimum (- 1, - 6)

Plug the extreme point

x = 0

into

4 x^{\frac{10}{3}} - 10 x^{\frac{4}{3}} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 1

into

4 x^{\frac{10}{3}} - 10 x^{\frac{4}{3}} \Rightarrow y = - 6

Minimum (1, - 6)

Minimum (- 1, - 6), Maximum (0, 0), Minimum (1, - 6)

f (x) = x^{2} + x - 30

f (x) = x^{2} + 8 x + 5

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

f (x) = \frac{x ^{2}}{x ^{4} + 16}

f (x) = - 2 x^{3} + 6 x^{2} + 12

What is the extreme f(x)=4(x^{(10/3)})-10(x^{(4/3)}) ?
The extreme f(x)=4(x^{(10/3)})-10(x^{(4/3)}) is Minimum(-1,-6),Maximum(0,0),Minimum(1,-6)