What is the equation of the line normal to #f(x)=4/(2x-1) # at #x=0#?
A normal line is a line that is perpendicular to the tangent. In other words, we must first find the equation of the tangent.
Step 1: Determine which point the function and the tangent pass through
Step 2: Differentiate the function
The derivative of
We can now use the quotient rule, as shown above, to determine the derivative.
Step 3: Determine the slope of the tangent
The slope of the tangent is given by evaluating
Then, we can say:
Step 4: Determine the slope of the normal line
As mentioned earlier, the normal line is perpendicular, but passes through the same point of tangency that does the tangent. A line perpendicular to another has a slope that is the negative reciprocal of the other. The negative reciprocal of
Step 5: Determine the equation of the normal line using point-slope form
We now know the slope of the normal line as well as the point of contact. This is enough for us to determine its equation using point-slope form.
The line normal to
Determine the equation of the normal lines to the given relations at the indicated point.
Hopefully this helps, and good luck!