What is the equation of the line that is normal to #f(x)=4x^3-3x^2+5x-2# at # x=1 #?
The slope of the normal at a given point is the negative inverse of the slope of the function at that point. i.e. if the slope of the function is
To find the slope, differentiate the function.
Therefore the slope of the normal is
The calculate the constant
Therefore the normal is