Question #11 Find the x-values of the absolute maximums and minimums for the function f(x) over the given interval. (6 points) f(x)=x' -6x3 +10 Interval: [1,5] Absolute Max: Absolute Min: Question #12 Find ~- for the following equation below. Use proper notation!! dx (6 points) y = (x +5)'Question #13 The cost of selling widgets is given by the cost function C(x) =4x +10 where x is the number of units sold. The price of each widget is given by the function p =50-.05x (6 points) A) How many widgets must be sold to maximize profit? B) What is the maximum profit? C) What price per widget must be charged in order to maximize profit?Question #14 An object is launched into the air. Its path is calculated using the function s(1) =-0.25t' +10t+5 where s(t) is the position of the object in feet and the variable "(" time in seconds. Find each of the following... (6 points) A) What is the position of the object at t = 4 seconds? B) What is the velocity of the object at t = 4 seconds? C) What is the acceleration of the object at t = 4 seconds? D) When does the object reach its maximum height? E) What is the maximum height of the object?Question #15 A rectangle is to have a perimeter of 60 ft. Find the dimensions of the rectangle such that the dimensions yield maximum area. (5 points)Milt A rectangular box with an open lap and square base is to have a volume of ll] . Find the dimensions of the box lhal will have minimum surface area. What will be the minimum surface area? Round all answers to 2 decimal places. (6 points)