This kind of question would actually be very dependable. So, let's suppose that we would have a number as 16. We would then have to divide this number by 4, mainly because we would want to find how many 4's would go into the number 16. But this would actually be an example. So, whatever math problem you may have, just remember this technique, how many numbers would go into that specific number.
(a)
![f'(x) = \frac{d}{dx}[\frac{lnx}{x}]](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Cfrac%7Blnx%7D%7Bx%7D%5D)
Using the quotient rule:
For maximum, f'(x) = 0;
(b) <em>Deduce:
</em>
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
, since ln(e) is simply equal to 1
Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
, as required.
A^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
