Chapter 3 Section 4

\[ \definecolor{ucrblue}{rgb}{0.0627,0.3843,0.6039} \definecolor{ucrgold}{rgb}{0.9686,0.6941,0.2824} \definecolor{ucrred}{rgb}{0.8941,0,0.1686} \definecolor{ucrgreen}{rgb}{0.4706,0.7451,0.1255} \definecolor{ucraccent}{rgb}{1.0000,0.9569,0.8392} \DeclareMathOperator*{\LO}{O} \DeclareMathOperator*{\Lo}{o} \DeclareMathOperator*{\Recip}{Recip} \DeclareMathOperator*{\abs}{abs} \DeclareMathOperator{\pow}{pow} \]

Notes

• Notes

Linguistic Mapping Exercises

• Linguistic Mapping Exercises PDF

Knowledge Checks

1. Determine the equation of the line that is tangent to the circle \(C\) at the point \((-1,2)\), where \(C\) is the circle that is given by the equation \[(x+2)^2+(y-4)^2=5.\]
2. Take \(f\) to be the quadratic function and \(L\) to be the line that are given by \[f(x)=3x^2-5x+1\quad\text{and}\quad L(x)=mx+b.\] Identify a quadratic equation that determines \(m\) so that \(L\) is tangent to \(f\) at \((2,3).\)
3. Find the the equation of the line \(L\) tangent to \(f(x)=3x^2-5x+1\) at \((2,3).\)
4. Determine the equation of the line \(L\) tangent to \(f(x)=10x^3-10x+5\) at \((1,5).\)

• Knowledge Checks PDF
• Knowledge Checks Solutions

Remember, do the knowledge checks before checking the solutions.

Practice Problems

• Practice Problems

Return

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