What is the extreme f(x)=x^{20}+4x^{10}+8 ?

The extreme f(x)=x^{20}+4x^{10}+8 is Minimum(0,8)

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extreme f(x)=x^{20}+4x^{10}+8

extreme points

f (x) = x^{20} + 4 x^{10} + 8

Minimum (0, 8)

Solution steps

Find the critical points:

x = 0

Domain of

x^{20} + 4 x^{10} + 8 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = 0

into

x^{20} + 4 x^{10} + 8 \Rightarrow y = 8

Minimum (0, 8)

f (x, y) = 5 x + 2 y

f (x) = 0.4 x^{2} - 192 x + 33821

y = 9 x^{4} - 4 x^{3}, (- 3, 3)

f (x) = \frac{x ^{2}}{x ^{2} - 108}

y = 2 x^{2} - 64 x

What is the extreme f(x)=x^{20}+4x^{10}+8 ?
The extreme f(x)=x^{20}+4x^{10}+8 is Minimum(0,8)