What is the equation of the normal line of #f(x)=x-x^2/2# at #x=2#?
Thus the point
Now the derivative
and evaluated at the point 2 we get
This means that the gradient of the function f at the point when x=-2 is -1.
Now a line normal at this point is perpendicular and will hence have a gradient of 1 since the product of gradients of perpendicular lines must be -1.
Bu t a normal line is still a straight line so has a linear equation of form
If we substitute the point (2,0) and the gradient 1 into this linear equation we get
Therefore the equation of the required normal line is