The normal line of a function #f# at #x=a# is the line perpendicular to the tangent line of #f# at #x=a#. Using the above definition and the fact that #g(-2) = -10#, find an equation of the normal line of the function #g# at #x = -2#?

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Answer 1 · 2017-03-14T00:41:14

#y=-1/(g'(-2))(x+2) - 10#

The slope of the tangent line to the graph of #g# at #x=-2# is #g'(-2)#.

The slope of a line perpendicular to that is #-1/(g'(-2))#

The equation of the line through #(-2,-10)# with slope #-1/(g'(-2))# is

#y-(-10) = 1/(g'(-2))(x+2)#.

In slope-intercept form the equation is:

#y=-1/(g'(-2))(x+2) - 10#