The parametric equations are x= e^t -1 and y=2e^t +3t
So dx/dt = e^t and dy/dt = 2e^t + 3
Let P be a point of curve C. Suppose the tangent line to C at the point P has slope 7. Find the coordinates of P
dy/dx = (2e^t + 3)/e^t = 7 so 7= 2+ 3/e^t and e^t = 3/5
Now I can then figure out that x = -2/5 but how do I figure out what y is?
y = 2e^t + 3t => y = 2(3/5) + 3t