What is the slope of the secant line that intersects the graph of \( g(x) = \frac{x}{x^2 + 1} \) at \( x =...
What is the slope of the secant line that intersects the graph of \( g(x) = \frac{x}{x^2 + 1} \) at \( x = 2 \) and \( x = 3 \)?
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info@snapandsolve.comTo find the slope of the secant line, calculate the difference quotient:
\[ g(2) = \frac{2}{2^2 + 1} = \frac{2}{4 + 1} = \frac{2}{5} \]
\[ g(3) = \frac{3}{3^2 + 1} = \frac{3}{9 + 1} = \frac{3}{10} \]
\[ \text{slope} = \frac{g(3) - g(2)}{3 - 2} = \frac{\frac{3}{10} - \frac{2}{5}}{1} = \frac{3}{10} - \frac{4}{10} = -\frac{1}{10} \]
The slope of the secant line is \(-\frac{1}{10}\).
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