The discussion focuses on finding the equation of a tangent line to the curve defined by y=e^x that passes through the origin (0,0). The derivative of the function, y'=e^x, is established as the slope of the tangent line at any point (x,y) on the graph. To determine the specific point x_0 where the tangent line intersects the origin, participants suggest using the tangent line formula y=e^{x_0}(x-x_0)+e^{x_0} and solving for x_0 such that the line passes through (0,0).
PREREQUISITESStudents studying calculus, particularly those learning about derivatives and tangent lines, as well as educators looking for examples of exponential function behavior.
iRaid said:Homework Statement
Find an equation for a line that is tangent to the grpah of y=ex and goes through the origin.
Homework Equations
The Attempt at a Solution
y'=ex
That's about all I can think of. I don't know how to make the tangent line go through the origin. Can someone lead me in the right direction?
Ray Vickson said:At any point (x,y) on the graph, how would you compute the slope of the tangent line?
RGV