Question

What is the slope of the tangent line to the parametric curve x = t2 + 2t, y = t2 + 1 at t = 1?

I tried to solve before and got 2, which was incorrect.

Thank you in advance!

Answer 1

1/2

Explanation:

x = t² + 2t

dx/dt = 2t + 2

y = t² + 1

dy/dt = 2t

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

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

dy/dx = t / (t + 1)

At t = 1, dy/dx = 1/2.