Expert: Paul Klarreich - 12/21/2011

Question
show that the curves y=e^-x and y=(e^-x)cosx are tangent to each other at each intersection point.

i got the derivatives of both which are:
dy/dx=-e^-x and
dy/dx=(-e^-x)cosx + (e^-x)(-sinx)

i don't know what to do after that, do i equate them to each other?

Answer
Questioner:humaira
Country:Ontario, Canada
Category:Calculus
Private:No
Subject:calculus: derivatives for trigonometry

Question:

show that the curves y=e^-x and y=(e^-x)cosx are tangent to each other at each intersection point.

i got the derivatives of both which are:
dy/dx=-e^-x and
dy/dx=(-e^-x)cosx + (e^-x)(-sinx)

i don't know what to do after that, do i equate them to each other?
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Interpret the vocabulary:

"Intersection point":  Set  e^-x = e^-x cos x  and solve for x.  Hint:  e^-x is never zero, so you can cancel it.  Then just solve  1 = cos x

"tangent to each other":  They have the same slope at those points.

Find dy/dx for each, substitute your intersections, etc.