consider F(x) = 1-e^x. Find the slope of the graph of f(x) at the point where the graph crosses the x-axis.

Question

chaise · Answer

I might be wrong but is the slope -1? Can anyone else concur?

anonymous · Answer

huh, how did you get that? :O

chaise · Answer

Differentiate the equation and substitute, you get -e^x. When the graph cuts the x axis, x is equal to zero.

-e^x
=-e^0
=-1

anonymous · Answer

To clarify, you use both F(x) and f(x) in your question, by f(x) do you mean the derivative of F(x), or did you mean them both to be the same?

chaise · Answer

I'm not sure if this is right, your question is a bit funny, which is what nbouscal is clarifying now.

anonymous · Answer

oh, I see, thank's chaise! there was a follow-up. could you help with that as well?
the question's this:
Find the equation of the tangent line to the curve at this point.

chaise · Answer

well, you know the slope of the equation is -1, and if the tangent is at the point where the original graph cuts the x axis, then the y intercept of the equation of the tangent will also be 0. The equation of the line is:

y=-1x+0

The y intercept is 0.