1. Calculus Applications of Maximum and Minimum

2. Practical Applications • D raw the diagram • Express the problem that needs to be maximised or minimised (often in terms of two variables) as an equation • L ink the two variables in the expression with an equation. There is uaually something else in the question linking the two variables. • Substitute for one variable in the expression using the link above. • Differentiate • Equate to zero so that you find the turning points. f’(x) = O and solve for x. • Back substituting into the original problem to find the maximum or minimum value. • Test your answer by rereading the question. It could be the problem wants both variables or the maximum value.

3. Example A wire frame is to constructed out of 1200 mm wire. Find the height and width of each of the equal sections so that the total area is as large as possible

4. 1200 mm of wire • Draw w www • h hhhh • Express • Area = height x whole width • = 4hw • Link the two variables • 1200 = 5h + 8w • Substitute • Differentiate • Equate to zero • Back • Test • No the answer called for the height h and width w, so the correct answer is