How do I find the equation for a tangent line without derivatives?
The equation of the tangent outoutcontinuity is the leavings when you divorce by (x-a)^2.
It's EASY for polynomials. You bear to explore the analytic geometry of polynomial dispersion and you obtain furnish that 1. dispersion by (x-a)(x-b) gives a leavings that is the secant outoutcontinuity intersecting the graph at x=a and x=b, 2. dispersion by (x-a)^2 yields a leavings which is the tangent outoutcontinuity at x=a. It's EASY for probable and algebraic discharges too. To feel probable or algebraic discharges, transcribe the discharge as a polynomial in two variables, x and y, as in F(x,y) = 0, and swell to primary adjust. That fist adjust equation is the equation for the tangent outline.