Question

What is the slope of the tangent line to the parametric curve x = t^2 + 2t, y = t^2 + 1 at t = 1? (4 points)

1/2

1/4

4

2

Answer 1

`(1)/(2)`

Step-by-step explanation

The given parametric curve has equation:

`x = {t}^(2) + 2t`

and

`y = {t}^(2) + 1`

Let us differentiate each equationtion with respect to t.

`(dx)/(dt) = 2t + 2`

and

`(dy)/(dt) = 2t`

The slope function is given by:

`(dy)/(dx) = ( (dy)/(dt) )/( (dx)/(dt) )`

This implies that:

`(dy)/(dx) = (2t)/(2t + 2)`

At t=1,

`(dy)/(dx) = (2(1))/(2(1)+ 2)`

`(dy)/(dx) = (2)/(4)`

`(dy)/(dx) = (1)/(2)`

The correct choice is A.