What is the extreme f(x)=\sqrt[3]{5x^3+5} ?

The extreme f(x)=\sqrt[3]{5x^3+5} is Saddle(0,\sqrt[3]{5})

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extreme f(x)=\sqrt[3]{5x^3+5}

extreme points

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

f (x) = x^{5} - 10 x^{4} - 1 = x^{4} (x - 10) - 1

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 4, - 2 \leq x \leq 5

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

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

f (x) = x^{2} - y^{2} + 21

What is the extreme f(x)=\sqrt[3]{5x^3+5} ?
The extreme f(x)=\sqrt[3]{5x^3+5} is Saddle(0,\sqrt[3]{5})