At what point on the curve y=1+2e^x-3x is the tangent line parallel to the line 3x-y=5?

1 Answer
Jun 8, 2017

(ln3,7-3ln3)

Explanation:

3x-y=5
y=3x+5

Here we have slope m=3 since it is in the form y=mx+b.
Since the lines are parallel, they have the same slope.

Find the derivative to find the point wih tangent line of slope 3:
y=1+2e^x-3x
y'=0+2e^x-3
3=2e^x-3
3=e^x
x=ln3

Find the y-coordinate.
y=1+2e^x-3x
y=1+2e^(ln3)-3ln3
y=7-3ln3

Thus it is parallel to the tangent line at the point (ln3,7-3ln3).