Precalc0110to0111-page25

Precalc0110to0111-page25 - (Section 1.11: Limits and...

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(Section 1.11: Limits and Derivatives in Calculus) 1.11.14 PART G: GRAPHING FUNCTIONS USING DERIVATIVES Example 5 (Profit; Revisiting Example 2) Again, Px () = ± x 2 + 200 x ± 5000 . Graph P . § Solution We will discuss how to graph quadratic functions such as P in Section 2.2. For now, we can use the derivative function ± P to help us graph P . • In Part D (Example 2, Form 4), we found that ± = ² 2 x + 200 . Think of this as a “ slope function ” that gives us slopes of tangent lines. • Find any point(s) on the graph where the tangent line is horizontal ; its slope is 0. Solve: ± = 0 ² 2 x + 200 = 0 x = 100 There is a horizontal tangent line at the point 100, P 100 , or 100, 5000 . WARNING 2
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