\( y=\frac{2 x+1}{x^{2}+6 x+5} \)
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Step 1: Identify the given function: \[ y = \frac{2x + 1}{x^2 + 6x + 5} \] Show more…
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Key Concepts
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$\begin{array}{l}{\text { a. Find an equation for the line that is tangent to the curve }} \\ {y=x^{3}-6 x^{2}+5 x \text { at the origin. }} \\ {\text { b. Graph the curve and tangent line together. The tangent }} \\ {\text { intersects the curve at another point. Use Zoom and Trace to }} \\ {\text { estimate the point's coordinates. }}\end{array}$ $\begin{array}{l}{\text { c. Confirm your estimates of the coordinates of the second }} \\ {\text { intersection point by solving the equations for the curve and }} \\ {\text { tangent line simultaneously. }}\end{array}$
Derivatives
Differentiation Rules
$$y=\frac{-5}{\left(2 x^{3}+1\right)^{2}}$$
Calculating the Derivative
The Chain Rule
$$y=\frac{2 x}{1+x^{2}}$$
Differentiation
Linearization and Differentials
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