How large should the squares cut from the corners be to make a box of largest volume? The corresponding numbers are x = 10 and (20 – x) = 10.Īn open top box is made from cutting small congruent squares from the corners of 6 inches by 6 inches sheet of paper and bending up the sides. Therefore when x = 10 we have an optimized maximum value of 100. The first Derivative is f( x) = 20 – 2 x. Step 4: Test the Critical Values and endpoints. Step 3: Draw the function on the interval from. Is closed on the interval, (0 ≤ x ≤ 20). We want the value of x that will make f ( x) as large as possible. The product of the two numbers will equal f( x). The other number must be (20 – x) since the two numbers sum to twenty. Step 2: Variable: x represents one of the numbers we are looking for. Use the first and second derivatives to identify and classify critical points (where f’ = 0 or does not exist).įind two positive numbers whose sum is 20 and whose product is as large as possible. Use what you know about the shape of the function’s graph and the physics of the problem.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |