Precalc0110to0111-page21

Precalc0110to0111-page21 - different forms of difference...

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(Section 1.11: Limits and Derivatives in Calculus) 1.11.10 PART D: FINDING DERIVATIVES Example 2 (Profit; Revisiting Examples 2-5 in Section 1.10) A company sells widgets. Assume that all widgets produced are sold. Let P be the profit function for the company; Px () is the profit (in dollars) if x widgets are produced and sold. Our model: Px () = ± x 2 + 200 x ± 5000 . Find the instantaneous rate of change of profit at 60 widgets. • We will ignore integer restrictions on x . § Solution We want to find ± P 60 () . We will present three solutions based on three
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Unformatted text preview: different forms of difference quotients we developed in Section 1.10. Form 2 P 60 ( ) = lim x 60 P x ( ) P 60 ( ) x 60 = lim x 60 140 x ( ) , x 60 ( ) by Ex.3 in Section 1.10 ( ) As x approaches 60, we see that 140 x approaches 140 60 ( ) , or 80. We can substitute x = 60 directly; the restriction x 60 ( ) is irrelevant here. = 140 60 ( ) = 80 dollars widget This is the slope of the red tangent line below....
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