A. Find the extrema of the following function on the given interval, if there are any, and determine the values of x at which the extrema occur. f(x) = x3 - 9x2 + 15x - 24 [1, 4] (3 pts) B. Solve the given problem involving optimization (7 pts) A rectangular field is to be fenced off along the bank river where no fence is required along the bank. If the material for the fence costs 60 pesos per running foot for the two ends and 90 pesos per running foot for the side parallel to the river, find the dimensions of the field of largest possible area that can be enclosed with 27,000 pesos worth of fence.Directions: Read each item carefully. Show all necessary solutions in solving. 1. Find the derivative of the following using implicit differentiation. a. x2 +y? = x+y b. x2 + xy3 = x C. y = sec(x + y) d. x cosy + y sin x - 1 = 0 e. 3 2 X 2. What is the slope of the line tangent to the curve 8x3 - y= = 4at the point (1,-2)