Section 1.4 We only know one point on the tangent line; therefore, determining the slope of the tangent line is not as straight- forward as determining the slope of the secant line (of which we know two points). Determining the slope of the tangent line to f(x) = x at the point P(1,1). What do we need? Choose another point Q and determine the Keep changing the Q (x,x) (1.5.. h m= y-y/ h to get closer to P msec What do we need? Choose another point Q and determine the Keep changing the Q (x,x) (1.5,) (1.1,. (1.01,. (1,______) (0.99, (0.9,_ (0.5,. h Difference Quotient: m= to get closer to P z-yi h msec The slope of the tangent line is the limit of the slopes of the secant lines. The goal is to get h closer to 0. f(x+h)-f(x) h