ants ts A box is to be made from a cardboard sheet measuring 15 in X 7 in, by cutting off square pieces from each corner and turning up the flaps at the end (see the diagrams below below). lastering 15 in 15 - 25 7 - 2x Tin 7 -23 15 -27 15- 27 Let the side of the squares cut off at each corner be x in. 1. (3 point) Express the volume V(x) as a function of x. What values of x are permissible in this situation? [This should be an interval.] 2. (4 points) Find V (x). Simplify your answer as much as possible. ns 3. (3 points) Find the critical values of V. Which of these critical values is in the interval of permissible values for x? 4. (3 points) What value of x will give the box of maximum volume among all the boxes made in this fashion? Explain the reason for your