Let C be the curve given parametrically by x = (t^3) - 3t; y = (t^2) - 5t
a) Find an equation for the line tangent to C at the point corresponding to t = 4
b) Determine the values of t where the tangent line is horizontal or vertical.
dy/dx = (dy/dt)/(dx/dt)
slope = d/dx of f(x,y)
equation of a line: y-y1 = m (x-x1)
The Attempt at a Solution
see attached - I know I need to solve for t, but I don't know how with these seemingly unsolvable equations because there is a t^3 and a t = 52 in the first equation and a t^2and a t = -4 in the second equation. Please help thanks!