What is the extreme f(x)=8x^4-5x^3+x^2-2x+3 ?

The extreme f(x)=8x^4-5x^3+x^2-2x+3 is Minimum(0.55765…,2.10223…)

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extreme f(x)=8x^4-5x^3+x^2-2x+3

extreme points

f (x) = 8 x^{4} - 5 x^{3} + x^{2} - 2 x + 3

Minimum (0.55765 \dots, 2.10223 \dots)

Solution steps

Find the critical points:

x \approx 0.55765 \dots

Domain of

8 x^{4} - 5 x^{3} + x^{2} - 2 x + 3 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0.55765 \dots,

Increasing

: 0.55765 \dots < x < \infty

Plug the extreme point

x = 0.55765 \dots

into

8 x^{4} - 5 x^{3} + x^{2} - 2 x + 3 \Rightarrow y = 2.10223 \dots

Minimum (0.55765 \dots, 2.10223 \dots)

f (x, y) = 400 - 81 x^{2} - 81 y^{2}

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

x^{4} + 2 x^{2}

f (x) = \frac{x}{x ^{2} + 25}, - 7 \leq x \leq 7

f (x) = 4 x^{2} + \frac{3000}{x}

What is the extreme f(x)=8x^4-5x^3+x^2-2x+3 ?
The extreme f(x)=8x^4-5x^3+x^2-2x+3 is Minimum(0.55765…,2.10223…)