What is the equation of the line that is normal to #f(x)= (2-x)- sqrt( 2x+2) # at # x=1 #?
Firstly we need a point at which the line intersects. We know that the line is tangent to
So we know the line passes through #(1,-1).
Next we will look at the gradient of the line. The gradient of the tangent is given by
We have used the chain rule to differentiate the second term. Now, substitute in a value of
Now that we have our gradient and a point the line passes through, the last thing to do is find the
Thus we now have the equation of the tangent line:
The graph below will further illustrate the situation.