Please write neatly and show all your work. I would also appreciate if you circle the answers. Thanks a lot

Show work Find the antiderivative of the following problems. 1. f(x) = 2x3 - 4x2 + 8x 2. f(x) = (x4 - sin x) 3. Use the first derivative test to find local extrema. f(x) = x3 - 3x2 - 9x - 1 4. You are trying to build a fenced-in corral next to a river. You wish to make it as big as possible but only have 100ft of fencing. What would be the dimensions of the corral with the largest possible area.5. Use the second derivative test to identify concavity and inflection points. f(x) = x4 + 4x3+ 14. Determine whether the Mean Value Theorem applies for the functions over the given interval [11, b]. y= 9 x2 over [-3, 3] 5. For the following exercises, evaluate the limits with L'Hopital's rule