Solution assignment 09 Tangent line to graph

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Assignment 9

The graph of the function:

y=e^x

intersects the Y-axis in point A.
The tangent line at this point of the graph intersects the X-axis. Calculate the coordinates of this intersection point.

Solution

Intersection point A has the coordinates (0,1). In order to calculate the tangent line at this point, we calculate the slope and we do this by differentiation:

y'=e^x

and thus the slope in the point (0,1) equals:

m=e^0=1

The tangent lne has the following equation:

y-y_0=m(x-x_0)

with:

(x_0,y_0)=(0,1) and m=1

and thus:

y-1=1(x-0)

or:

y=x+1

This line intersects the X-axis in the point (-1,0).

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