Show all work No late acceptance!! Solve all problems using the methods learned in chapters 2.9,3.4, 3.5 &3.8 I will not accept answers that do not show calculus solutions la. Determine the local linear approximation of (x)sin(3x) near x-0 lb. Approximateusing the method of local linear approximation (2.05) 2. Determine the extrema for the following functions over the indicated intervals: 3. a) Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by the conclusion of the theorem. f(x)-1-r2/3 1,1] b) Determine if MVT applies to the following function on the given interval. If so, find the find the poin(s) that are guaranteed to exist by the conclusion of the theorem. f(x) =2x-- [3,6] The surface area of a cube is to be calculated from the measured value of its side, what is the maximum possible percentage error in the measurement if the percentage error in the calculation of the surface area is to be kept within ± 1.5% 4- The hypotenuse of a right triangle is measured to be 12 cm with a possible error of ±1/2 cm. a) What is the error in the calculation of the angle θ, if the side adjacent to θ is known to 5. be exactly 6 cm? b) What is the maximum possible percentage error in the measurement of the adjacent side and the calculation of If fertilizer made from N pounds of Nitrogen and P pounds of Phosphate is used on an acre of farmland then the yield of com (in bushels per acre) is given by the following: Y =75 + 6N +7 P-N2-2p2 + NP If nitrogen costs $0.25/lb and phosphate costs $0.20/lb, which combination of N and P produces the highest yield of corn if the farmer intends to spend $30/acre? 6. A closed rectangular box with a volume of 18000 in' is to be made so its base is a rectangle with length 3 times its width. Find the dimensions that will minimize the surface area. 7.