Question

Find an equation of a line that is tangent to the curve and is parallel to the line definition of a derivative

1. The equation of line of tangent is :
y=1/2x+7/2 and y=1/2x-1/2.
According to the statement
we have to find the equation of the line with the help of the given curve.
So, For this purpose, we know that the
The given information is:
The equations of the tangent lines to the curve is y= (x-1)/(x+1) and the that are parallel to the line x-2y = 2.
So,
A line parallel to x-2y = 2 must have the same slope. The slope of this line is 1/2.
So we want the slope of the tangent line to be 1/2.
Now we find the derivative of the y= (x-1)/(x+1)
So,
By quotient rule the derivative become
y’= (x(x+1)-(x-1)*1)/(x+1)^2
y’ = 2/(x+1)^2
So,
Now find the value of the x with the help of y’.
So,
2/(x+1)^2 = 1/2
And solve it then
x = 1 and -3.
So, x = 1 and x = -3.
Now, the value of y become:
At x = 1, y = 0 and
x = -3, y = 2.
then
The equation of lines with point (1,0) and slope 1/2.
And The equation of lines with point (-3,2) and slope 1/2.
So, The equation of line of tangent is :
y=1/2x+7/2 and y=1/2x-1/2.