What is the equation of the normal line of #f(x)=5x^4+3x^3+x^2-2x-4# at #x=1#?
Differentiate the function to find its gradient.
Use the point
The gradient of the normal is the negative reciprocal of the gradient of the tangent at a point.
So the gradient of the normal at
To find the coordinates of the point the normal passes through, substitute
So coordinates are
Equation of a line is: