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Popular Functions >

extreme ln(x^2+x+1)

Solution

extreme points

ln (x^{2} + x + 1)

Solution

Minimum (- \frac{1}{2}, ln (\frac{3}{4}))

Solution steps

f^{'} (x) = \frac{2 x + 1}{x ^{2} + x + 1}

Find intervals:

Decreasing

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

Increasing

: - \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

ln (x^{2} + x + 1) : ln (\frac{3}{4})

Minimum (- \frac{1}{2}, ln (\frac{3}{4}))

Graph

Popular Examples

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

extreme f(x)=2x^3-6x+5

extreme (1/2-x^2+y^2)e^{1-x^2-y^2}

extreme f(x)=2xln(9x)

extreme f(x,y)=-x^4+y^4+x^2-y^2

Frequently Asked Questions (FAQ)

What is the extreme ln(x^2+x+1) ?
The extreme ln(x^2+x+1) is Minimum(-1/2 ,ln(3/4))