Find an equation of the tangent line to the given curve at the specified point.
\[
y=\frac{x^{2}}{3+x}, \quad\left(1, \frac{1}{4}\right)
\]
\[
y=
\]

Answer

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Answer

\(y = \frac{7x}{16} - \frac{3}{16}\)

Steps

Step 1 ：Find the derivative of the given function: \(y = \frac{x^2}{3+x}\)

Step 2 ：Evaluate the derivative at the specified point \((1, \frac{1}{4})\)

Step 3 ：Use the point-slope form of a line to find the equation of the tangent line

Step 4 ：\(y = \frac{7x}{16} - \frac{3}{16}\)