9. At what point on the curve x = 3t^2 + 7, y = t^3 − 6 does the tangent line have slope 1/2 ?

Answer 1

dy/dx = (dy/dt) / (dx/dt) = 3t²/6t = (1/2)t

So, (1/2)t = 1/2. Thus, t = 1

When t = 1, x = 3t² + 7 = 10 and y = t³ - 6 = -5

The point of tangency is (10, -5)