MATH 203 Final Examination December 2017 Page 2 of 3 [10] 5. Consider the function y 2 V1 + 2:17. (3) Use the denition of derivative to nd the formula for dy/dx. (b) Find the linearization L(m) of the function y(a:) at a = 4 (c) Use this linearization to approximate the exact value of \\/ 10. [7] 6. 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. [8] 7. (3) Verify that the point (2,1) belongs to the curve dened by the equation d :92 + rim/3 + y = 1 + :172, and nd the implicit derivative dy at this point. :1; (b) Write the equation of the tangent line to the curve at the point (2,1). :17 15 8. thh b'lt t f = (a) 1n ea soueexremao f(:17) $2_$+1 on the interval [0, 3]. (b) The length of a rectangle is increasing at the rate of 8 cm/ s and its width is increasing at the rate of 5 cm/ s. When the length is 20 cm and the Width is 12 cm, how fast is the area of the rectangle increasing at that instant? l 1 2 (c) Use l7H6pital7s rule to evaluate the lim M 3H0 1 cos(2a:) [11] 9. (3) Find the point (cymyo) on the line 3/ = 2 2:17 that is closest to the point (5,2). (b) If A = 1200 cm2 of material is available to make a box with a square base and an open top, nd the largest possible volume of the box