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Popular Functions >

extreme x^3+2x^2+x+1

Solution

extreme

Solution

Maximum (- 1, 1), Minimum (- \frac{1}{3}, \frac{23}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 4 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} + 2 x^{2} + x + 1 : 1

Maximum (- 1, 1)

Plug

x = - \frac{1}{3}

into

x^{3} + 2 x^{2} + x + 1 : \frac{23}{27}

Minimum (- \frac{1}{3}, \frac{23}{27})

Maximum (- 1, 1), Minimum (- \frac{1}{3}, \frac{23}{27})

Graph

Popular Examples

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extreme f(x,y)=x^6-3x^2y^2+3xy^3

extreme-x^3+x^2+8x+8

extreme f(x)=-3x^3+27x

Frequently Asked Questions (FAQ)

What is the extreme x^3+2x^2+x+1 ?
The extreme x^3+2x^2+x+1 is Maximum(-1,1),Minimum(-1/3 , 23/27)