Finding an equation of a graph

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SUMMARY

The discussion centers on finding equations for a graph with specified turning points at (0,0) and (60,10). Two potential equations provided are a quartic function, y=7.7*10^7 (x)^2 (x - 120)^2, and a cubic function, y=4.6*10^-5 (x)^2 (x-120). Participants emphasize the importance of showing work to facilitate understanding and highlight the relationship between a function and its derivative in determining the function from known derivative values.

PREREQUISITES
  • Understanding of polynomial functions, specifically quartic and cubic equations.
  • Knowledge of calculus concepts, particularly derivatives and their significance.
  • Familiarity with graphing techniques and identifying turning points.
  • Basic algebra skills for manipulating equations and solving for variables.
NEXT STEPS
  • Research how to derive polynomial equations from given turning points.
  • Learn about the relationship between a function and its derivative in calculus.
  • Explore methods for graphing quartic and cubic functions effectively.
  • Study techniques for determining the coefficients of polynomial equations based on specific conditions.
USEFUL FOR

Students in mathematics, educators teaching calculus, and anyone interested in graph theory and polynomial functions will benefit from this discussion.

thestormbreaker
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I need help with finding an equation of a graph. I was wondering if anyone was able to give me an equation to a graph that has a turning point at (0,0) (or a gradient of zero at (0,0)) and a turning point at (60,10). It would be great if you could show you basic working out so I can see how you came to your answer.

y=7.7*10^7 (x)^2) (x - 120)^2 This is one in quartic
y=4.6*10^-5 (x)^2 (x-120) This is one in cubic


There is more than one answer and I was hoping for as many as people could come up with.

If anyone could help it was be very much appreciated.

Thanks
 
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is it a one dimensional function och two dimensional?

Also you "must" show us your work done so far, your thougts and ideas so we can help you. It is no point for us just show how we would do then you copy us..

one question: what is the relationsship between function and derivative? If you know what value the derivative has at one point, how can you determine the function?
 

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