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Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4), Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

Solution steps

f^{'} (x) = 3 x^{2} - 8 x + 3

Find intervals:

Increasing

: - \infty < x < \frac{- 7 + 4}{3},

Decreasing

: \frac{- 7 + 4}{3} < x < \frac{7 + 4}{3},

Increasing

: \frac{7 + 4}{3} < x < \infty

Plug

x = \frac{4 - 7}{3}

into

x^{3} - 4 x^{2} + 3 x : - 7 + \frac{41 7 - 128}{27} + 4

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4)

Plug

x = \frac{4 + 7}{3}

into

x^{3} - 4 x^{2} + 3 x : 7 + \frac{- 128 - 41 7}{27} + 4

Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4), Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

Popular Examples

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extreme f(x,y)=x^2+xy+y^2-16y+85 extreme points

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extreme f(x,y)=-4x^2+7xy-3y^2+x+y extreme points

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Frequently Asked Questions (FAQ)

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