Function Expression :
\[f(x)=\frac{10x}{7x+10} \]Domain
\[\left]-\infty, - \frac{10}{7}\right[ \cup \left]- \frac{10}{7}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{10}{7} \]\[\lim_{x \overset{<}{\rightarrow- \frac{10}{7}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow- \frac{10}{7}} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{10}{7} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{70 x}{\left(7 x + 10\right)^{2}} + \frac{10}{7 x + 10} \]\[f^{\,\prime}(x)=\frac{100}{\left(7 x + 10\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{10 x}{7} - \frac{100 \log{\left(7 x + 10 \right)}}{49} \]Sign Table
Variation Table
Plot
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