Answer:
The interval of increase of g(x) is 
.
Step-by-step explanation:
The interval of increase occurs when first derivative of given function brings positive values. Let be 
, the first derivative of the function is:
The following condition must be met to define the interval of increase:
The first term is always position due to the quadratic form, the second one is a first order polynomial and it is known that positive value is a product of two positive or negative values. Then, the second form must satisfy this:
The solution to this inequation is:
Now, the solution to this expression in interval notation is:
F(x)=2x/(x-1)
Denominator cannot be equal 0.
x-1=0
x=1 is vertical asymptote.
To find horizontal asymptote
we need divide the coefficients before x
y=2x/x=2,because when x becomes really big (x---->∞) , value of 1 will not influence the result .
y=2 is horizontal asymptote
Take the derivative with respect to t
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
divide by w
we add sin(wt) to both sides
divide both sides by cos(wt)
OR
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be
since 2npi is just the period of cos
substituting our second soultion we get
since 2npi is the period
so the maximum value =
minimum value =
2 by 7 + – is equals to 1 so we can say that x.
x=1-2/7
x=7/7-2/7
x=5/7
