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Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 6), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 6 - 43)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3} + 1,

Decreasing

: - \frac{2}{3} + 1 < x < \frac{2}{3} + 1,

Increasing

: \frac{2}{3} + 1 < x < \infty

Plug

x = \frac{3 - 2 3}{3}

into

x^{3} - 3 x^{2} - x + 1 : \frac{12 3 - 20}{3 3} + 43 - 6

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 6)

Plug

x = \frac{3 + 2 3}{3}

into

x^{3} - 3 x^{2} - x + 1 : \frac{12 3 + 20}{3 3} - 6 - 43

Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 6 - 43)

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 6), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 6 - 43)

Popular Examples

extreme f(x)=sqrt(9-x^2)extreme points

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intercepts of (-3x(x-2))/((x-2)(x+2))intercepts

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inverse of f(x)=(4/5)^x inverse

f (x) = (\frac{4}{5})^{x}

Frequently Asked Questions (FAQ)

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