Derivatives Consider the following parametric curves.

a. Determine dy/dx in terms of t and evaluate it at the given value of t.

b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.

x = 2 + 4t, y = 4 − 8t; t = 2

Solution 45E

Step 1: To obtain the derivative we need which we can also write as Evaluating andseparately, we get

Putting the valuesand into evaluate , we get

.Hence the value of is which is independent of t.