Long time no question on add maths in homework forum.
Find the x-intercept(s) of y = ln x - (x/e).
Hi,
A good question that requires thinking. Students should attempt. Thanks for sharing!
Cheers,
Wen Shih
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x is definitely e but im curious how we can prove this thing.. =X
Hi,
Consider the derivative. Thanks!
Cheers,
Wen Shih
lol i see... but how do we know if there exists a maxima point and it just nice touches the x-intercept in the 1st place, without finding the dy/dx?
Hi,
We may not know the behaviour of a non-standard curve, so there is a need to investigate. Thanks!
Cheers,
Wen Shih
haha..ok. thanks for sharing
Besides differentiating it, it's easier to set y = 0?
Apologise for the previous comment, it was incomplete.
Let's look at the rate of growth of each of the two terms.
For 0 < x <= 1, ln x grows very fast, but for x > 1, ln x grows slowly. On the other hand, the growth of x/e is linear (with gradient 1/e).
This suggests that there will be a maxima...
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