Quote Originally Posted by Invader View Post
An electron moving along the x axis has a position given by x = 12te^(-2.1 t) m, where t is in seconds. How far is the electron from the origin when it momentarily stops?



The answer is 2.102m, but I only know that because I understand that I need to find the derivative of x = 0 for t (x's slope will be 0 when it 'stops moving'). Time t will give me the position in the original equation. The actual values I got only because I know a thing or two about getting around my calculator, but I want to know how to take the derivative of the original equation on paper. Can anyone show me how to do this?


[EDIT]: dx/dt = (12 - 25.2t)e^(-2.1t) is that correct? If so, then my next problem involves getting t onto one side of the equation so that I can solve for it.
You shouldn't have to solve for t here if you only want the zeros. 0 is special because if f(x)y(x) = 0 then you can be sure that f(x)=0 or g(x) = 0. so you need to find the zeros of f(x) = 12 - 25.2t and g(x) = exp(-2.1t)

g doesn't have any roots and f is linear so it only has one which is 12/25.2 to whatever accuracy you have. I never can remember the significant digits thing.

That would be a very hard problem to solve if you needed to get a function for t. You'd just want to use newtons method probably.