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I'm having a little trouble solving a problem on my calc. homework. I'm not very proficient with my ti-83, which is why I'm having a problem. The problem I'm working on has two parts...

"The aerobic rating of a person x years old is modeled by the function...

A(t)=110[ln(x)-2]/x for x >= 10

a) At what age is a person aerobic rating largest?"

I understand that I am to take the derivative of the function, and set it equal to zero in order to maximize it, which results in...

(x*110[1/x] - 110[ln(x)-2] (1))/x^2

which simplifies into A'(t) = (110 - 110[ln(x)-2])/x^2 = 0

I can work this out on paper, but I'm not too confident with my abillity to do logarithms (which this requires), so I was wondering if anyone could explain how to solve this on the ti-83.

The second part of the question reads...

"b) At what age is a person's aerobic rating decreasting most rapidly?"

I know that I am now supposed to take the derivative of the derivative...

A''(t) = (x^2[110(1/x)]-[110-110[ln(x)-2]]*2x)/x^4

This problem I can't work out on paper (I tried and failed many times). The tutor at school recommended I just do this on the calculator, but again, I don't know how to do that. When I plug the A'' equation into Y1 on my graphing calculator and graph it, according to the calculator y = 0 at 11, but I know that's not right. The correct answer is 33 (approximately), but I don't know how to get it. Any information would be greatly appreciated. Thanks

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# Calc question (derivatives)

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