What is the equation of the line normal to # f(x)=(x-1)^2/(x^2+2) # at # x=1#?
By definition, the normal line must have a slope that is the opposite reciprocal of the slope of the tangent line at
Thus, to determine the slope of the normal line, we must first calculate the slope of the tangent line at x=1, which is just the derivative of
Step 1: Calculate
Step 2: Find f'(1)
Step 3: Determine the equation of the normal line
The equation for the vertical tangent line is