SOLUTION: What are the coordinates (x,y) for the highest point on the graph of the function f(x) = (e^6x)/[(e^9x) + 4]? Work: I see that the problem is asking for the absolute max of the

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Question 1052764: What are the coordinates (x,y) for the highest point on the graph of the function f(x) = (e^6x)/[(e^9x) + 4]?
Work: I see that the problem is asking for the absolute max of the problem and to find it I need to take the first and second derivatives to find where the slope are zeros, but I don't know where to start taking the derivative. I have tried using the quotient rule to take the derivative but don't seem to get work that leads to the simplification of the problem. I am unsure if there are exponential/natural log rules that can apply to simplify the problem.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!


df%2Fdx=%28e%5E%286x%29%28-3e%5E%289x%29%2B24%29%29%2F%28e%5E%289x%29%2B4%29%5E2
df%2Fdx=-3%28e%5E%286x%29%28e%5E%289x%29-8%29%29%2F%28e%5E%289x%29%2B4%29%5E2
So the derivative equals zero when,
e%5E%289x%29-8=0
e%5E%289x%29=8
9x=ln%288%29
x=ln%288%29%2F9
x=ln%282%5E3%29%2F9
x=%283ln%282%29%29%2F3%5E2
x=ln%282%29%2F3
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