Find Equation for Tangent Line to y=e^x at Origin

[iRaid]

Homework Statement

Find an equation for a line that is tangent to the graph of y=e^x and goes through the origin.

Homework Equations

The Attempt at a Solution

y'=e^x

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]

Homework Statement

Find an equation for a line that is tangent to the grpah of y=e^x and goes through the origin.

Homework Equations

The Attempt at a Solution

y'=e^x

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?

At any point (x,y) on the graph, how would you compute the slope of the tangent line?

RGV

 

[iRaid]

At any point (x,y) on the graph, how would you compute the slope of the tangent line?

RGV

Find the derivative at that point.

 

[HallsofIvy]

And you have already said that the derivative is again e^x.

So the tangent line to y= e^x at x= x_0 would be y= e^{x_0}(x- x_0)+ e^{x_0}. Now, what must x_0[/b] be so that goes through (0, 0)?

 

[iRaid]

0? Not really sure..