(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.
Answer:
6a−14
Step-by-step explanation:
If <em>x</em> = 4.338338338…, then
1000<em>x</em> = 4338.338338338…
and subtracting <em>x</em> from this eliminate the trailing decimal.
1000<em>x</em> - <em>x</em> = 4338.338338338… - 4.338338338…
999<em>x</em> = 4334
<em>x</em> = 4334/999
area=legnth times width
we notice this is a special case
(a+b)(a-b)=a^2-b^2
area=(a+3b)(a-3b)=a^2-9b^2
area=a^2-9b^2
I believe that it's (1,3)
(tip: with these problems, try to use desmos.com)
