Input y = 8 x^2 Geometric figure parabola Alternate form y – 8 x^2 = 0 Root x = 0 Derivative (d)/(dx)(8 x^2) = 16 x Global minimum min{8 x^2} = 0 at x = 0

Input y = 8/x Geometric figure hyperbola Alternate form assuming x and y are positive x y = 8 Roots (no roots exist) Derivative (d)/(dx)(8/x) = -8/x^2 Limit lim_(x-> ± infinity) 8/x = 0