You have to get the fractions to have a common denominator in order to add them together. what you want to do it multiply the whole number (ex. 3) by the denominator of the fraction (2/3) then add the numerator to have an improper fraction. the first trail would be 11/3 and the second trail would be 17/6. find the common denominator, add the two fractions, and then simplify the fraction the most you can.
Printed pages in 11 minutes = 33 pages
Printed pages in a minute = 33/11
= 3 pages/minute
Take the deritivive
remember
the deritivive of f(x)/g(x)=(f'(x)g(x)-g'(x)f(x))/(g(x)^2)
so
deritiveive is ln(x)/x is
remember that derivitive of lnx is 1/x
so
(1/x*x-1lnx)/(x^2)=(1-ln(x))/(x^2)
the max occurs where the value is 0
(1-ln(x))/(x^2)=0
times x^2 both sides
1-lnx=0
add lnx both sides
1=lnx
e^1=x
e=x
see if dats a max or min
at e/2, the slope is positive
at 3e/2, the slope is negative
changes from positive to negative at x=e
that means it's a max
max at x=e
I realize I didn't find the max point, so
sub back
ln(x)/x
ln(e)/e
1/e
the value of the max would be 1/e occuring where x=e
4th option is answer (1/e) because that is the value of the maximum (which happens at x=e)