What is the extreme f(x)=x^6+4x^5+10 ?

The extreme f(x)=x^6+4x^5+10 is Minimum(-10/3 ,-192710/729),Saddle(0,10)

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extreme f(x)=x^6+4x^5+10

extreme points

f (x) = x^{6} + 4 x^{5} + 10

Minimum (- \frac{10}{3}, - \frac{192710}{729}), Saddle (0, 10)

Solution steps

f^{'} (x) = 6 x^{5} + 20 x^{4}

Find intervals:

Decreasing

: - \infty < x < - \frac{10}{3},

Increasing

: - \frac{10}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{10}{3}

into

x^{6} + 4 x^{5} + 10 : - \frac{192710}{729}

Minimum (- \frac{10}{3}, - \frac{192710}{729})

Plug

x = 0

into

x^{6} + 4 x^{5} + 10 : 10

Saddle (0, 10)

Minimum (- \frac{10}{3}, - \frac{192710}{729}), Saddle (0, 10)

F (x, y) = 2 x^{5} + x^{3} y^{2} + 6 x y^{4}

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

f (x) = - 6 x^{2} + 30 x - 36

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

f (x, y) = - 8 x y + 2 x^{4} + 2 y^{4}

What is the extreme f(x)=x^6+4x^5+10 ?
The extreme f(x)=x^6+4x^5+10 is Minimum(-10/3 ,-192710/729),Saddle(0,10)