What is the extreme x^{19/9}+x^{10/9} ?

The extreme x^{19/9}+x^{10/9} is Maximum(-10/19 ,(-10/19)^{19/9}+(-10/19)^{10/9}),Minimum(0,0)

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extreme x^{19/9}+x^{10/9}

extreme points

x^{\frac{19}{9}} + x^{\frac{10}{9}}

Maximum (- \frac{10}{19}, (- \frac{10}{19})^{\frac{19}{9}} + (- \frac{10}{19})^{\frac{10}{9}}), Minimum (0, 0)

Solution steps

Find the critical points:

x = - \frac{10}{19}, x = 0

Domain of

x^{\frac{19}{9}} + x^{\frac{10}{9}} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - \frac{10}{19},

Decreasing

: - \frac{10}{19} < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = - \frac{10}{19}

into

x^{\frac{19}{9}} + x^{\frac{10}{9}} \Rightarrow y = (- \frac{10}{19})^{\frac{19}{9}} + (- \frac{10}{19})^{\frac{10}{9}}

Maximum (- \frac{10}{19}, (- \frac{10}{19})^{\frac{19}{9}} + (- \frac{10}{19})^{\frac{10}{9}})

Plug the extreme point

x = 0

into

x^{\frac{19}{9}} + x^{\frac{10}{9}} \Rightarrow y = 0

Minimum (0, 0)

Maximum (- \frac{10}{19}, (- \frac{10}{19})^{\frac{19}{9}} + (- \frac{10}{19})^{\frac{10}{9}}), Minimum (0, 0)

- 10 x^{4} + 4 x^{2} - 6

f (x) = \frac{( e ^{x} )}{1 + x ^{2}}

f (x) = 2 (4 x)^{x}

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

y = sin (x) cos (x)

What is the extreme x^{19/9}+x^{10/9} ?
The extreme x^{19/9}+x^{10/9} is Maximum(-10/19 ,(-10/19)^{19/9}+(-10/19)^{10/9}),Minimum(0,0)