(Section 1.11: Limits and Derivatives in Calculus) 1.11.14 PART G: GRAPHING FUNCTIONS USING DERIVATIVESExample 5 (Profit; Revisiting Example 2)Again, Px()=±x2+200x±5000. Graph P. § SolutionWe will discuss how to graph quadraticfunctions such as Pin Section 2.2. For now, we can use the derivativefunction ±Pto help us graph P. • In Part D (Example 2, Form 4), we found that ±=²2x+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: ±=0²2x+200=0x=100There is a horizontal tangent line at the point 100,P100, or 100, 5000. WARNING 2
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