What is the equation of the line normal to # f(x)=2(x-1)^2-2x+4# at # x=-3#?

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Answer 1 · 2017-05-25T22:58:11

#y = x/18 + 41 + 5/6#

#f(x) = 2x^2 - 6x + 6#

#f'(x) = 4x - 6#

#f'(-3) = -12 - 6 = - 18#

We want a line #y = 1/18 x + b#, where #(-3, f(-3))# is one of its points.

#f(-3) = 2*9 + 18 + 6 = 42#

#42 = 1/18 (-3) + b#

#b = 42 - 1/6 = 41 + 5/6#