What is the equation of the line normal to # f(x)=sqrt(1/(x^2+2) # at # x=1#?
in simplifying the equation we get
We then apply the chain rule to get
Then we substitute in 1 for x to find the gradient of the tangent at x=1
This results us getting
Now we know the gradient, we just need the co-ordinates which it runs through. We then sub x=1 back int the original equation to find the point which the normal will pass through. The y value, after subsitution is
Therefore by substituting the numbers/values into the point gradient formula, we'll find the equation of the normal. The point gradient formula is