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Popular >

extreme f(x)=x^3-6x^2+4x-2

Solution

extreme points

f (x) = x^{3} - 6 x^{2} + 4 x - 2

Solution

Maximum (\frac{2 ( 3 - 6 )}{3}, \frac{288 - 112 6}{9} + 166 - 42), Minimum (\frac{2 ( 3 + 6 )}{3}, \frac{288 + 112 6}{9} - 42 - 166)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x + 4

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = \frac{2 ( 3 - 6 )}{3}

into

x^{3} - 6 x^{2} + 4 x - 2 : \frac{288 - 112 6}{9} + 166 - 42

Maximum (\frac{2 ( 3 - 6 )}{3}, \frac{288 - 112 6}{9} + 166 - 42)

Plug

x = \frac{2 ( 3 + 6 )}{3}

into

x^{3} - 6 x^{2} + 4 x - 2 : \frac{288 + 112 6}{9} - 42 - 166

Minimum (\frac{2 ( 3 + 6 )}{3}, \frac{288 + 112 6}{9} - 42 - 166)

Maximum (\frac{2 ( 3 - 6 )}{3}, \frac{288 - 112 6}{9} + 166 - 42), Minimum (\frac{2 ( 3 + 6 )}{3}, \frac{288 + 112 6}{9} - 42 - 166)

Popular Examples

extreme f(x,y)=ln(x)+ln(y)-ln(x+y)-x/(12)-y/3 extreme points

f (x, y) = ln (x) + ln (y) - ln (x + y) - \frac{x}{12} - \frac{y}{3}

extreme f(x,y)=8x^4+y^2-16xy extreme points

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extreme f(x)=e^{-(x^2+y^2)}extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-6x^2+4x-2 ?
The extreme f(x)=x^3-6x^2+4x-2 is