What is the equation of the normal line of #f(x)=x^3 + 3x^2 + 7x - 1 # at #x=-1 #?
The gradient function is the first derivative
So the gradient when X=-1 is 3-6+7=4
The gradient of the normal , perpendicular, to the tangent is
If you are not sure about this draw a line with gradient 4 on squared paper and draw the perpendicular.
So the normal is
But this line goes through the point (-1,y)
From original equation when X=-1 y=-1+3-7-1=6