MATH 203 Final Examination December 2018 Page 2 of 3 [10] 6. Consider the function y = V25 + :17. (3) Use the denition of derivative to nd the formula for dy/dzr. (b) Find the linearization L(m) of the function y(a:) at a = 0 (c) Use this linearization to approximate \\/ 30. [8] 7. Let f(:17) = :153 235+ 3. (a) Find the slope m of the secant line joining the points (2, f(2)) and (0, f(0)) (b) Find all points :1: = c (if any) on the interval [-2,0] such that f'(c) m. [17] 8. (a) Verify that the point (2,1) belongs to the curve dened by the equation :1:2 + 2g2 + 2 = :133 ff, and nd an equation of the tangent line to the curve at this point. (b) A 13ft ladder is leaning against a vertical wall of a house when its base starts to slide away (in horizontal direction) from the wall. By the time when the base is at the distance a: = 5 ft from the wall the base is moving at the rate of dm/dt = 2 ft /sec. How fast is the top of the ladder sliding down the wall at that instant? 7 , 7' , xsin(3:1:) (c) Use 1 HQpltal s rule to evaluate the 015ng) (629\" _ D2. :1:+2 x2+5 [11] 9. (3) Find the absolute maximum and absolute minimum of f(m) = on the interval [13]. (b) Find the radius 7" and the height h of a cylindrical can closed on both top and bottom that has a given volume V, but has the smallest possible surface area A (rst express h as a function of 7")