Please reread what you have posted.
Is it exactly as it appears in your text book? (What is the text?)
It just does not seem to be correct.
Hi. I'm taking an Analysis I course and we just started differentiation. I'm not 100% comfortable with it yet and would appreciate some help on a problem in my textbook. Suppose that f:[0,1] to R is continuous on f(0)= 0, differentiable for x in [0,1], and 0 <= f '(x) <= af(x) for a > 0. Prove that f = 0. (Hint: consider the derivative of (e^(-ax))f(x).) Any help you offer would be greatly appreciated.
It has that f --- 0 where --- is three horizontal lines on top of each other (basically an equal sign with an extra line). I figured this meant equals, but I guess it does not. What exactly does it mean and how would you solve this? Thank you for trying to help.
Yikes. I did make a serious mistake. It should be: Suppose that f:[0,1] to R is continuous with f(0)= 0, differentiable for x in [0,1], and 0 <= f '(x) <= af(x) for a > 0. Prove that f = 0. (Hint: consider the derivative of (e^(-ax))f(x).)
I'm using a textbook outside of class just to study. It's called Elementary Real Analysis by Brian S. Thomson.
He isn't being a grouch. He simply wants to see evidence that you are doing something to try to solve the problem. Hence even if you have no work to show, you could mention what you have tried to do to solve the problem.
And, as most members here don't know how to use LaTeX, you can post your work in the following kind of format:
-ae^{ - ax} f(x) + e^{ - ax} f'(x) = e^{ - ax} (- af(x) + f'(x)} ) <= e^{ - ax} ( - af(x) + af(x))
It's harder to read, but still quite understandable.
-Dan