Chapter 3 Section 4

Notes

Linguistic Mapping Exercises

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 \((1,5).\)

Remember, do the knowledge checks before checking the solutions.

Practice Problems

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