What is the extreme f(x)=x^{2/9}(7x+11) ?

The extreme f(x)=x^{2/9}(7x+11) is Maximum(-2/7 ,9(-2/7)^{2/9}),Minimum(0,0)

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extreme f(x)=x^{2/9}(7x+11)

extreme points

f (x) = x^{\frac{2}{9}} (7 x + 11)

Maximum (- \frac{2}{7}, 9 (- \frac{2}{7})^{\frac{2}{9}}), Minimum (0, 0)

Solution steps

f^{'} (x) = \frac{11 ( 7 x + 2 )}{9 x ^{\frac{7}{9}}}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{7},

Decreasing

: - \frac{2}{7} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{2}{7}

into

x^{\frac{2}{9}} (7 x + 11) : 9 (- \frac{2}{7})^{\frac{2}{9}}

Maximum (- \frac{2}{7}, 9 (- \frac{2}{7})^{\frac{2}{9}})

Plug

x = 0

into

x^{\frac{2}{9}} (7 x + 11) : 0

Minimum (0, 0)

Maximum (- \frac{2}{7}, 9 (- \frac{2}{7})^{\frac{2}{9}}), Minimum (0, 0)

3 x + \frac{75}{x}

x^{2} - y^{2} - 6 x + 6 y + 2

\frac{2 x ^{2} - 8}{- x ^{2} - 2 x + 3}

f (x) = 6 x - \frac{1}{7 x}

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

What is the extreme f(x)=x^{2/9}(7x+11) ?
The extreme f(x)=x^{2/9}(7x+11) is Maximum(-2/7 ,9(-2/7)^{2/9}),Minimum(0,0)