Finding an equation of a graph

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The discussion revolves around finding an equation for a graph with specific turning points at (0,0) and (60,10). Participants provide examples of quartic and cubic equations, such as y=7.7*10^7 (x)^2 (x - 120)^2 and y=4.6*10^-5 (x)^2 (x-120). There is an emphasis on the importance of showing work and thought processes to facilitate better assistance. Additionally, a question is raised about the relationship between a function and its derivative, particularly how knowing the derivative at a point can help determine the function. Overall, the thread seeks collaborative input to derive multiple valid equations.
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?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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