What is the extreme f(x)=2x^4-27x^3+118x^2-142x-104 ?

The extreme f(x)=2x^4-27x^3+118x^2-142x-104 is Minimum(0.80778…,-155.08846…)

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extreme f(x)=2x^4-27x^3+118x^2-142x-104

extreme points

f (x) = 2 x^{4} - 27 x^{3} + 118 x^{2} - 142 x - 104

Minimum (0.80778 \dots, - 155.08846 \dots)

Solution steps

Find the critical points:

x \approx 0.80778 \dots

Domain of

2 x^{4} - 27 x^{3} + 118 x^{2} - 142 x - 104 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0.80778 \dots,

Increasing

: 0.80778 \dots < x < \infty

Plug the extreme point

x = 0.80778 \dots

into

2 x^{4} - 27 x^{3} + 118 x^{2} - 142 x - 104 \Rightarrow y = - 155.08846 \dots

Minimum (0.80778 \dots, - 155.08846 \dots)

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

f (x) = x e^{- 9 x}, 0 \leq x \leq 2

y = \frac{x ^{3}}{x ^{2} - 1}

s

f (x) = 2 cos (x) + sin^{2} (x)

What is the extreme f(x)=2x^4-27x^3+118x^2-142x-104 ?
The extreme f(x)=2x^4-27x^3+118x^2-142x-104 is Minimum(0.80778…,-155.08846…)