What is the extreme f(x)=x^{12/5}-6x^{2/5}+2 ?

The extreme f(x)=x^{12/5}-6x^{2/5}+2 is Minimum(-1,-3),Maximum(0,2),Minimum(1,-3)

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extreme f(x)=x^{12/5}-6x^{2/5}+2

extreme points

f (x) = x^{\frac{12}{5}} - 6 x^{\frac{2}{5}} + 2

Minimum (- 1, - 3), Maximum (0, 2), Minimum (1, - 3)

Solution steps

f^{'} (x) = \frac{12 x ^{2} - 12}{5 x ^{\frac{3}{5}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{\frac{12}{5}} - 6 x^{\frac{2}{5}} + 2 : - 3

Minimum (- 1, - 3)

Plug

x = 0

into

x^{\frac{12}{5}} - 6 x^{\frac{2}{5}} + 2 : 2

Maximum (0, 2)

Plug

x = 1

into

x^{\frac{12}{5}} - 6 x^{\frac{2}{5}} + 2 : - 3

Minimum (1, - 3)

Minimum (- 1, - 3), Maximum (0, 2), Minimum (1, - 3)

10 x - 5 x ln (x)

f (x) = x + 4 x^{- 1}

y = I n 9 - 2 x^{2}

f (x) = 2 x^{3} - 33 x^{2} + 144 x

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

What is the extreme f(x)=x^{12/5}-6x^{2/5}+2 ?
The extreme f(x)=x^{12/5}-6x^{2/5}+2 is Minimum(-1,-3),Maximum(0,2),Minimum(1,-3)