2x^3+x^2+1 - Wolfram|Alpha

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.

Input

2 x^3 + x^2 + 1

Plot

Plot

Plot

Alternate form

(x + 1) (2 x^2 - x + 1)

(2 x + 1) x^2 + 1

1/8 (-4 i x + sqrt(7) + i) (4 i x + sqrt(7) - i) (x + 1)

Real root

x = -1

Complex roots

x = 1/4 - (i sqrt(7))/4

x = 1/4 + (i sqrt(7))/4

Roots in the complex plane

Roots in the complex plane

Polynomial discriminant

Δ = -112

Properties as a real function

Domain

R (all real numbers)

Range

R (all real numbers)

Surjectivity

surjective onto R

Derivative

d/dx(2 x^3 + x^2 + 1) = 2 x (3 x + 1)

Indefinite integral

integral(2 x^3 + x^2 + 1) dx = x^4/2 + x^3/3 + x + constant

Local minimum

$min{2 x^3 + x^2 + 1} = 1 at x = 0$

Local maximum

$max{2 x^3 + x^2 + 1} = 28/27 at x = -1/3$

POWERED BY THE WOLFRAM LANGUAGE