en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme f(x)=-x^3+6x^2+x-1

Solution

extreme points

f (x) = - x^{3} + 6 x^{2} + x - 1

Solution

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 49 - 839), Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 49 + 839)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x + 1

Find intervals:

Decreasing

: - \infty < x < - \frac{13}{3} + 2,

Increasing

: - \frac{13}{3} + 2 < x < \frac{13}{3} + 2,

Decreasing

: \frac{13}{3} + 2 < x < \infty

Plug

x = - \frac{- 6 + 39}{3}

into

- x^{3} + 6 x^{2} + x - 1 : \frac{46 39 - 288}{9} + 49 - 839

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 49 - 839)

Plug

x = \frac{6 + 39}{3}

into

- x^{3} + 6 x^{2} + x - 1 : \frac{- 288 - 46 39}{9} + 49 + 839

Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 49 + 839)

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 49 - 839), Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 49 + 839)

Graph

Popular Examples

extreme y=(x^3)/(x^2-4)

extreme f(x)=1-e^{-kx}

extreme f(x,y)=x^2-y^2-2x+4y+6

extreme 1/(x+1)

extreme f(x)=x^2+4x+4,-4<= x<= 0

Frequently Asked Questions (FAQ)

What is the extreme f(x)=-x^3+6x^2+x-1 ?
The extreme f(x)=-x^3+6x^2+x-1 is