The equation is with the point

I used the chain rule (I hope I used it correctly)

,

,

The problem is I don't know how to find the equation for the tangent line to the curve at the given point.

- Oct 22nd 2007, 04:33 PMFalconPUNCH!Chain Rule Derivative (Finding the equation for the tangent line)
The equation is with the point

I used the chain rule (I hope I used it correctly)

,

,

The problem is I don't know how to find the equation for the tangent line to the curve at the given point. - Oct 22nd 2007, 05:19 PMgalactus
That's the product rule, not the chain rule.

If x=1, then the slope at that point is

Now, use your given points in y=mx+b to find the line equation. - Oct 22nd 2007, 06:53 PMFalconPUNCH!
- Oct 22nd 2007, 07:51 PMtopsquark
Okay, so you have the slope of the tangent line at the point where x = 1. What is the y value of this point?

Thus the tangent line at x = 1 has a slope of and touches the curve at the point . (There are a couple of 1/e's floating around. Make sure you keep track of them.)

So your line equation, becomes

at the point .

Plug this x and value into the line equation and solve for b.

-Dan - Oct 22nd 2007, 08:23 PMFalconPUNCH!
- Oct 22nd 2007, 08:39 PMtopsquark
- Oct 22nd 2007, 08:58 PMFalconPUNCH!
- Oct 22nd 2007, 09:01 PMtopsquark