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Let $y=a^x$ and $y=b^x$. How could I find the angle at the function intersection point? Thank you

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I'll do a bit: pnt of intersection =(0,1) – ABC Apr 8 '13 at 16:39
The most naive approach to this problem points out that a pair of intersecting lines divides the plane up into four V-shaped regions. Which one of these do you measure for its vertex angle? – Lubin Apr 8 '13 at 17:40
up vote 3 down vote accepted

Hint: After you find the slopes, you may find the formula $\tan(x+y)=\frac{\tan x+\tan y}{1-\tan x\tan y}$ useful, in the variant form $\tan(x-y)=\frac{\tan x-\tan y}{1+\tan x\tan y}$.

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First, you need to find the intersection point. Can you do that? Then find the slope of each curve by taking the derivative and evaluating at that point. The slope is the tangent of the angle from the $x$ axis, so take the arctangents of the slopes and subtract. You have the angle between the curves.

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