90x^4+63x^3-58x^2-40x - 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.

Step by step solutions marketing image

Step-by-Step Solutions with Pro

Get a step ahead with your homework

Input

90 x^4 + 63 x^3 - 58 x^2 - 40 x

Plot

Plot

Plot

Alternate form

x (6 x + 5) (5 x - 4) (3 x + 2)

x (x (x (90 x + 63) - 58) - 40)

x (90 x^3 + 63 x^2 - 58 x - 40)

Roots

x = -5/6

x = -2/3

x = 0

x = 4/5

Polynomial discriminant

Δ = 16734009600

Properties as a real function

Domain

R (all real numbers)

Range

{y element R : y>=-21.0471}

Derivative

d/dx(90 x^4 + 63 x^3 - 58 x^2 - 40 x) = 360 x^3 + 189 x^2 - 116 x - 40

Indefinite integral

integral(90 x^4 + 63 x^3 - 58 x^2 - 40 x) dx = 18 x^5 + (63 x^4)/4 - (58 x^3)/3 - 20 x^2 + constant

Global minimum

$min{90 x^4 + 63 x^3 - 58 x^2 - 40 x}≈-21.047 at x≈0.51620$

Local maximum

$max{90 x^4 + 63 x^3 - 58 x^2 - 40 x}≈5.8244 at x≈-0.28443$

Definite integral area below the axis between the smallest and largest real roots

integral_(-5/6)^(4/5) (-40 x - 58 x^2 + 63 x^3 + 90 x^4) θ(40 x + 58 x^2 - 63 x^3 - 90 x^4) dx = -168966847/16200000≈-10.4301

Definite integral area above the axis between the smallest and largest real roots

integral_(-5/6)^(4/5) (-40 x - 58 x^2 + 63 x^3 + 90 x^4) θ(-40 x - 58 x^2 + 63 x^3 + 90 x^4) dx = 196/81≈2.41975

POWERED BY THE WOLFRAM LANGUAGE

Related Queries:

Have a question about using Wolfram|Alpha?Contact Pro Premium Expert Support »

Give us your feedback »