What is the slope of the line normal to the tangent line of #f(x) = secxcos3x # at # x= (pi)/12 #?
1 Answer
Slope of normal:
Explanation:
since we know that the derivative of
if
therefore,
therefore, the point at which the normal passes is
^ this simplifies to:
therefore, the slope of the tangent is
since the slope of the normal is the negative reciprocal to the slope of a line, the slope of the normal will be:
Slope of normal:
Side note:

I simplified a few things and skipped those steps purposely so that this question doesn't run forever

I would say the hardest part about this question would be the simplification such as figuring out what
#tan(pi/12)# is or what#sec(pi/12)# is