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)
Answer:
m = 2.5
Step-by-step explanation:
m + 4 = 6.5
m= 6.5 - 4
m= 2.5.
Answer:
y = (x - )² -
Step-by-step explanation:
Given
y = (x + 2)(x - 3) ← expand factors
= x² - x - 6
Use the method of completing the square
add/ subtract ( half the coefficient of the x- term )² to x² - x
y = x² + 2(- ) x + - - 6
= (x - )² -
X+2y=18
-x -x
2y=-x+18
/2 /2 /2
y=mx+b
y=-1/2x+9
the slope is -1/2
Answer:
A=2(wl+hl+hw)=2·(9·12+3·12+3·9)=342
Step-by-step explanation: