Answer:
it is in the picture
Step-by-step explanation:
you just find the coordinates
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)
The slope intercept form of this would be y=*3x-1. The formula for slope intercept form is y=mx+b, where m is the slope and b is the y-intercept. I this problem, the y-intercept is -1, so you would plug in -1 for b, so the equation is y=mx-1. The slope is -3, so you plug that in for m, so the equation now becomes y=-3x-1. Hope that helps!!
