10.1Parametric FunctionsGreg Kelly, Hanford High School, Richland, Washington
In chapter 1, we talked about parametricequations.Parametric equations can be used to describe motion that is not a function.(29(29xftyg t==If fand ghave derivatives at t, then the parametrized curve also has a derivative at t. →
The formula for finding the slope of a parametrized curve is:dydydtdxdxdt=This makes sense if we think about canceling dt.
The formula for finding the slope of a parametrized curve is:dydydtdxdxdt=We assume that the denominator is not zero.→
To find the secondderivative of a parametrized curve, we find the derivative of the first derivative:dydtdxdt′=22d ydx(29dydx′=1.Find the first derivative (dy/dx).2. Find the derivative of dy/dxwith respect to t.3. Divide by dx/dt.→
Example 2 (page 514):2232Find as a function of if and .d ytxttyttdx=-=-→
Example 2 (page 514):2232Find as a function of if and .