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Ryan, Engineer

Category: Calculus and Above

Satisfied Customers: 9062

Experience: B.S. in Civil Engineering

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Discuss how you would use derivatives to help predict the various

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Discuss how you would use derivatives to help predict the various life cycle stages of this curve from development all the way through decline JA: The Advanced Math Tutor can help you get an A on your homework or ace your next test. Tell me more about what you need help with so we can help you best. Customer: Discuss how you would use derivatives to help predict the various life cycle stages of this curve from development all the way through decline JA: Is there anything else important you think the Advanced Math Tutor should know? Customer: no JA: OK. Got it. I'm sending you to a secure page on JustAnswer so you can place the $5 fully-refundable deposit now. While you're filling out that form, I'll tell the Advanced Math Tutor about your situation and then connect you two.

Ok, no problem. I'm not sure what material you have covered in your course, nor am I completely sure about how you are supposed to fit your particular curve into the discussion, but hopefully the following will help as a starting point. We can continue to discuss the topic after you read the following: With respect to a graph, a derivative is the slope of the tangent line to the graph at a particular point. Points on the graph where the derivative is positive indicate growth. The positive derivative means that the tangent line is sloping upward going from left to right across the graph, which means that the points on the graph are increasing in the vertical direction. Points on the graph where the derivative is small (that is, close to 0) indicate that growth is stalled and the function value (market share in the case of your particular graph) has leveled off and is remaining more or less constant. The slope of the tangent line to the graph in these areas is close to horizontal, which means that the points on the graph are not changing very much in the vertical direction. The graph in this region will appear to be "flat". And points on the graph where the derivative is negative represent decline. For these points, the slope of the tangent line is negative, which means that the tangent line is sloping downward as you move from left to right across the graph. The points on the graph will be decreasing in the vertical direction in this region, which means that the function is declining. While both curves in your graph have some of each type of point, it is not particularly helpful to zone in on any one particular point. It is a general trend that is important. For instance, looking at the blue line, the trend is generally positive (growth) for the first 26 or 27 days. Even though there are a few small dips in there, overall the derivatives in this region are positive, and the curve shows growth. From around day 29 to around day 39, the trend is mostly downward, with a little bit of "up". This is somewhat the reverse of the earlier portion of the graph. Even though there is some short-term growth in this interval, the trend is mostly a decline. Most of the derivatives in this interval would be negative. Let me know if that all makes sense to you, and please feel free to ask if you need more information or any clarification. Thanks, Ryan