Chapter 4.4 Practice

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Questions

1. For each ellipse \(E\) and point \(p\) on \(E\), determine the equation of the line that is tangent to \(E\) at \(p\).
   1. \(E\) given by the equation \(\frac{x^2}{4}+\frac{y^2}{9}=5\), \(p=\left(-4,3\right)\)
   2. \(E\) given by the equation \(\frac{(x+4)^2}{5}+\frac{(y-2)^2}{4}=9\), \(p=\left(1,6\right)\)
2. For each root function \(f\), and point \(p\), determine the line \(L\) that is tangent to \(f\) at \(p\)
   1. \(f(x)=\sqrt[4]{x}\), \(p=(16,2)\)
   2. \(f(x)=\sqrt[3]{x}\), \(p=(64,4)\)

Answers

1. 1. \(y=3x+15\)
   2. \(y=-x+7\)
2. 1. \(y=\frac{1}{32}x+\frac{3}{2}\)
   2. \(y=\frac{1}{48}x+\frac{8}{3}.\)

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