\f1. Multiple choice. Circle the option corresponding to the correct answer. No work needs to be shown. No partial credit will be given for an incorrect answer. (a) (5 points) Below, is a graph of a function f(r) on the interval [0, 5]. Define a function g (x ) = [ f(t) at. On what interval(s) is g(r) decreasing? (A) (0, 2) (B) (1,3) (C) (2, 4) (D) (4, 5) (b) (5 points) Suppose that Newton's Method is used to approximate the solution to the equation cos(r) - 2x = 0. If the initial guess is taken to be 21 = ;, then zz equals (A) (B) 3 (C) (D) *Math 1271-001 Exam 3 - Page 7 of 7 April 20, 2022 4. Use the Fundamental Theorem of Calculus to calculate the derivatives of the following functions. (a) (5 points) g(x) = / sin(2t) at (b) (5 points) f(x) = / (1+13) atMath 1271-001 Exam 3 - Page 4 of 7 April 20, 2022 2. (20 points) A box with a square base and open top must have a volume of 500 cm'. Find the dimensions of the box that minimize the amount of material used.Math 1271-001 Exam 3 - Page 3 of 7 April 20, 2022 (c) (5 points) Which of the following is equal to eltz de? (A) lim 1+12 (B) lim 2+1 310 310 IM= IM=IM= IM (C) lim 2+12 (D) lim el+zil