Complete parts a through c for the given function. 2 f(x)=x3(x1)on[1,1] (E a. Locate the critical point(s) of f. Select the correct choice below and. if necessary, fill in the answer box to complete your choice. V 2 The critical point(s) is(are) at X: 30 . (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) The function does not have a critical value. b. Use the First Derivative Test to locate the local maximum/maxima and minimum/minima values. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. '55 A- The local minimum/minima is/are at x = and there is no local maximum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) '3' B- The local maximum/maxima is/are at X: and the local minimum/minima is/are at X: (Use a comma to separate answers as needed. Type integer or simplified fractions.) 'C' C- The local maximum/maxima is/are at x = and there is no local minimum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) {1 D. There is no local maximum and there is no local minimum. a. A rectangular pen is built with one side against a barn. lf 400 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular Barn pens against a barn, each with an area of 100 m2 (see figure). What are the dimensions of each pen that minimize the amount of 100 100 100 100 fence that must be used? E) a. LetA be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in a form that does not include the length of the side parallel to the barn. A=j (Type an expression.) A rectangle is constructed with its base on the diameter A of a semicircle with radius 2 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area? (3 Let A be the area of the rectangle. What is the objective function in terms of the base of the rectangle, x? A = Cl (Type an expression.) A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 343 cubic feet. The concrete for the base costs $8 per square foot, the material for the roof costs $3 per square foot, and the material for the sides costs $5.50 per square foot. Find the dimensions of the most economical shed. E) Let x represent the length of one of the sides of the base and let C represent the cost of the shed. What is the objective function? C=D (Type an expression.) a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. Iapproximation - exactl c. Compute the percent error in the approximation, 100 . , where the exact value |exact| is given by a calculator. f(x) = 23' at a = 0; 0.03) a. L(X) = I Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. f(x) = e10x . . . dy = dx (Type an exact answer in terms of e.)Evaluate the following limit. Use I'Hopital's Rule when it is convenient and applicable. 2 + 7+ 10 lim X- -5-45-4x + x2 . . . Use I'Hopital's Rule to rewrite the given limit so that it is not an indeterminate form. X2 + 7x+ 10 lim = lim X- -5-45-4x + X X- -5