What is the equation of the line normal to # f(x)=-(x+6)(x+3)+4x^2-8x+2# at # x=0#?
To find the slope of the normal line, we need to differentiate to get
Differentiate using the product rule and power rule:
Plug in zero:
Find opposite reciprocal of tangent line slope to get normal line slope:
Equation of normal line (point-slope form):