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**asweet1** Let f(x)=x^80/e^x= x^80*e^-x. A graph of y= f(x) is shown below. There is clearly a local maximum point somewhere around x= 75 (actually the extree point is to the right of x=75). Also there appears to be at least one local minimum between x=-15 and x=45.

Use calculus to find the exact location of the local maximum that is near x=75 show that there is a local minimum at x=0.

I cannot show the grow however i can tell you that the y range goes by .5*10^116. However after that the exponents remain at 117 rather than 116. The x range goes by 15 starting at -30 going up to 150. Also I can see that the local max according to the graph is at coordinates (80, 3.1*10^117).

How would i figure this out? Would I find the slope of the tangent line?