Function Expression :
\[f(x)=ln(x+2 )+ln(-x+8 )-ln16 \]Domain
\[\left]-2, 8\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow8} }f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{x + 2} - \frac{1}{8 - x} \]\[f^{\,\prime}(x)=\frac{2 \left(x - 3\right)}{\left(x - 8\right) \left(x + 2\right)} \]
\[ \]
Integral
\[F(x) = x \log{\left(8 - x \right)} + x \log{\left(x + 2 \right)} - x \log{\left(16 \right)} - 2 x - 8 \log{\left(8 - x \right)} + 2 \log{\left(x + 2 \right)} \]Sign Table
Variation Table
Plot
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