Finding formula for a Perpendicular line to a Tangent

Question

Consider the graph of the function f(x)=3x^2-12x+14. What is the graph of the line perpendicular to the tangent line of this graph when x=3? 

 

Here's what I figured:

f'(x)=6x-12

f'(3)=6(3)-12

6=m in y=mx+b, therefore, the slope of the perpendicular line of the tangent is -1/6.

 

From here, how can I get the formula for this line? 

Answer 1

Just use the point where the tangent line intersects f(x):

 

x = 3 gives you f(3) = 2(9) - 12(3) + 14 = -4

 

Use (3, -4) to solve for b, the y-intercept.