Unformatted text preview: x , using the relationships between them. Then rewrite the equation in Step 2 as the equation of x , for example, Q = f ( x ). • 4. Write the domain of the function f . • 5. Find the ﬁrst derivative f of f . • 6. Find critical numbers of f by setting f ( x ) = 0. • 7. If the domain of f is a closed interval [ a,b ], use the Closed Interval Method to ﬁnd the absolute maximum or minimum value of f (i.e., compare the values of f at the critical numbers in Step 6 and at the endpoints a,b ). • 8. Otherwise, use the First Derivative Test to ﬁnd the absolute minimum or maximum value of f . Note An alternative method for solving optimization problems is to use implicit diﬀerentiation. Examples Example 1 of Section 4.7 (textbook): Example 2 of Section 4.7 (textbook): Example 3 of Section 4.7 (textbook): Example 4 of Section 4.7 (textbook): Example 5 of Section 4.7 (textbook): 1...
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 Fall '08
 Noohi
 Calculus, Ms. Hoa Nguyen, [email protected]

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