How do you find the equation of tangent line to the curve #y = 6x tan(x)# at x = π?

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Answer 1 · 2017-02-04T01:40:24

#y = 6pi(x-pi)#. See the overall and tangent-specific Socratic graphs.

graph{(6xtanx-y)(22x-y-60)=0 [-20, 20, -10, 10]}
graph{(6xtanx-y)(22x-y-65)=0 [0, 4, -50, 50]}

#y = 0, at x = pi#.

#y'=6x(tanx)'+6tanx (x)'=6xsec^2x+6tanx#

= at #P(pi, 0)#.

So, the equation to the tangent at #P(pi, 0)# is

#y-0=6pi(x-pi)#, giving

#6pix-y-6pi^2=0#