1. ## exponential function

At what point on the given curve is the tangent line parallel to the line 3x - y = 2? y = 3 + 2ex5x

How do i do this?

2. Originally Posted by rhcp1231
At what point on the given curve is the tangent line parallel to the line 3x - y = 2? y = 3 + 2ex5x

How do i do this?
You need to set the derivative of the curve to the slope of the given line and solve for x. By the way is 2e^x or 2ex?

3. 2e^x

so the derivative is 2e^x-5, how do i solve for x for that?

4. Originally Posted by rhcp1231
2e^x

so the derivative is 2e^x-5, how do i solve for x for that?
$\displaystyle 3=2e^x-5$

$\displaystyle 8=2e^x$

$\displaystyle e^x=4$

$\displaystyle x=ln(4)$

Then just plug that into the original equation for the curve and you have the point where te tangent line is parallel to the given line.

5. Originally Posted by Keithfert488
$\displaystyle 3=2e^x-5$

$\displaystyle 8=2e^x$

$\displaystyle e^x=4$

$\displaystyle x=ln(4)$

and the 3 comes from 3x - y = 2 right?

6. Originally Posted by rhcp1231
and the 3 comes from 3x - y = 2 right?
Yes. If you put the equation into slope intercept format (y=mx+b) you find that y=3x-2 so the slope is three.

7. Originally Posted by Keithfert488
Yes. If you put the equation into slope intercept format (y=mx+b) you find that y=3x-2 so the slope is three.
sweet thanks for the help