Find the smallest value (or explain why it doesn't exist) of g(x) = (9/x) x - 3 on [1,9].

Question

I could use some help with this one. What do you think? I would think that it does exist because we are given "on [1,9]". I assume "on [1,9]" means that we are looking for the minimum value for g(x) that occurs when x is between 1 and 9 - although i have never seen it put like that ("on [1,9]") have you? if we were only looking for the minimum value with no restraint then that would be undefined because we would be looking for -(9/x^2), the derivative of g(x), to be equal to zero which is undefined. please let me know your thoughts on this one and let me know if you think I am not on the right track with what i have said above. thank you so much. I think that the answer is 3.

Answer 1

to find the min (or max) take the derivative

dy/dx = 0 = -9/x^2 + 1 (assuming the space is a "+")

>>>>>> You have -9/x^2, what happened to the 1?

x^2 = 9 and x=3 or -3

The answer is x=3 since it is between 1 and 9. and the slope is negative the left of it and positive to the right so this is a minimum

The fact that the derivative (and the function) go to infinity at x=0 is not really significant when finding the minimum