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Popular Functions >

extreme y=x^3+x^2-x

Solution

extreme

Solution

Maximum (- 1, 1), Minimum (\frac{1}{3}, - \frac{5}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

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

Increasing

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

Plug

x = - 1

into

x^{3} + x^{2} - x : 1

Maximum (- 1, 1)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x : - \frac{5}{27}

Minimum (\frac{1}{3}, - \frac{5}{27})

Maximum (- 1, 1), Minimum (\frac{1}{3}, - \frac{5}{27})

Graph

Popular Examples

extreme f(x)=sqrt(x)-\sqrt[3]{x}

extreme f(x)=ln(x^2+7x+14),-4<= x<= 1

extreme f(x)=(x-1)/(x-2)

extreme f(x)=2x^2-36ln(x)

extreme y=x^2-8x+12

Frequently Asked Questions (FAQ)

What is the extreme y=x^3+x^2-x ?
The extreme y=x^3+x^2-x is Maximum(-1,1),Minimum(1/3 ,-5/27)