We say that the slope of the tangent line is the limit of the slopes of the secant lines, and we express this symbolically by writing the following.

lim Q -> p (mPQ) = m and lim x -> 1 (4x⁴ - 4/x - 1) = ____

Assuming that this is indeed the slope of the tangent line, we use the point-slope form of the equation of a line (see Appendix B) to write the equation of the tangent line through (1, 4) as the following

y - (___) = (___)(x - 1) or y = (___)x -(___)