Q14 of 149 Page 16

Write the angle between the curves y = e–x and y = ex at their point of intersection.

Given that y = e–x …(1) and y = ex ….(2)


Substituting the value of y in (1),


e–x = ex


⇒ x = 0


And y = 1 (from 2)


On differentiating (1) w.r.t. x, we get




On differentiating (2) w.r.t. x, we get




∵ m1× m2 = -1


Since the multiplication of both the slopes is -1 so the slopes are perpendicular to each other.


∴ Required angle = 90°


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