What is the extreme x^4+2x^3+6x^2-9x+12 ?

The extreme x^4+2x^3+6x^2-9x+12 is Minimum(0.54637…,9.28911…)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^4+2x^3+6x^2-9x+12

extreme points

x^{4} + 2 x^{3} + 6 x^{2} - 9 x + 12

Minimum (0.54637 \dots, 9.28911 \dots)

Solution steps

Find the critical points:

x \approx 0.54637 \dots

Domain of

x^{4} + 2 x^{3} + 6 x^{2} - 9 x + 12 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0.54637 \dots,

Increasing

: 0.54637 \dots < x < \infty

Plug the extreme point

x = 0.54637 \dots

into

x^{4} + 2 x^{3} + 6 x^{2} - 9 x + 12 \Rightarrow y = 9.28911 \dots

Minimum (0.54637 \dots, 9.28911 \dots)

f (x) = ∣ 2 x - 4 ∣

y (t, x) = - 2 t + x

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

g (x) = y (x - 3) (- x + 1)

f (x) = t (1 - t)

What is the extreme x^4+2x^3+6x^2-9x+12 ?
The extreme x^4+2x^3+6x^2-9x+12 is Minimum(0.54637…,9.28911…)