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How can I find the angle which the function $f(x)=e^x$ meets the $y$ axis? I think it is the slope of $y$ at the point $(0,1)$. Is that right?

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up vote 2 down vote accepted

Hint: The slope is absolutely relevant, but it's not the final answer; remember, you're looking for the angle. For example, a slope of $2$ (not that this is the slope in your case) would correspond to an angle of $60^\circ$, because that is the slope of a $30^\circ$-$60^\circ$-$90^\circ$ right triangle in this position:

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Slope of $f(x)=e^x$ at $(0,1)$ represents $\tan \theta$ where $\theta$ is the angle between curve and $x-$axis. To find you need to first find $\theta=\arctan(\frac{dy}{dx}_{(0,1)})$ and then required angle would be $\pi/2-\theta$

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Thank you for your help. – Basil R Mar 8 '13 at 6:35

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