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Popular >

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}))

Popular Examples

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

f (x, y) = - x^{3} - y^{2} + 6 x y + 2

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

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

extreme f(x)= x/(ln(x)),2<= x<= 5 extreme points

f (x) = \frac{x}{ln ( x )}, 2 \leq x \leq 5

extreme f(x)=x^{4/3}-2x^{1/3}extreme points

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

extreme x/(x^2+12x+35)extreme points

\frac{x}{x ^{2} + 12 x + 35}

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))