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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x + 1 : - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1)

Plug

x = \frac{2}{3}

into

x^{3} - 2 x + 1 : (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1

Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Popular Examples

domain of f(x)= 1/2 (3)^{x+4}-5 domain

f (x) = \frac{1}{2} (3)^{x + 4} - 5

intercepts of f(x)=x^2(x-4)(x^2+6)intercepts

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

asymptotes of f(x)=(x^2-2x-3)/(x-2)asymptotes

f (x) = \frac{x ^{2} - 2 x - 3}{x - 2}

domain of f(x)=(6+x)/(1-6x)domain

f (x) = \frac{6 + x}{1 - 6 x}

intercepts of f(x)=2x-5 intercepts

f (x) = 2 x - 5

Frequently Asked Questions (FAQ)

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