MAT 126 Final: F08finalsol

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 126
• Professor: All

Document Summary

3x2. (a) use the de nition of derivative to nd f (x) if f (x) = x2 x. F (x + h) f (x) h. = lim h 0 (x + h)2 (x + h) (x2 x) x2 + 2xh + h2 x h x2 + x. = lim h 0 h h(2x + h 1) h. = lim h 0 (2x + h 1) = 2x 1. (b) using any method, give an equation for the tangent line to y = x2 x at the point (1, 0). The tangent line at (a, f (a)) is given by y f (a) = f (a)(x a). F (a) = f (1) = 0 and f (1) = 2 1 1 = 1. Therefore the line is y = 1(x 1), i. e. y = x 1: (16 pts) a fertilizer company has to construct cylindrical storage tanks, pictured below. V = r2h = 16 , in cubic meters.