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Subsection 1.1.2 Exercises

Exercises — Stage 1

1

On the graph below, draw:

  1. The tangent line to \(y=f(x)\) at \(P\text{,}\)
  2. the tangent line to \(y=f(x)\) at \(Q\text{,}\) and
  3. the secant line to \(y=f(x)\) through \(P\) and \(Q\text{.}\)
2

Suppose a curve \(y=f(x)\) has tangent line \(y=2x+3\) at the point \(x=2\text{.}\)

  1. True or False: \(f(2)=7\)
  2. True or False: \(f(3)=9\)
3

Let \(L\) be the tangent line to a curve \(y=f(x)\) at some point \(P\text{.}\) How many times will \(L\) intersect the curve \(y=f(x)\text{?}\)