Question

At what point on the curve
y = 9 + 2ex − 6x is the tangent line parallel to the line 6x − y = 1?

Answer 1

the curve is y = 9 + 2e^x -6x??

Answer 2

Sorry, yes the curve is y = 9 + 2e^x - 6x

Answer 3

I got the point is (ln3 , 3-6ln3) . Since it's weird, I am not sure.

Answer 4

Thanks for the help, but I don't think this is the correct point..

Answer 5

what's the slope of the line? can you calculate it?

Answer 6

the slope is 6

Answer 7

what's the slope of the function, i.e., the derivative?

find the x that makes them the same.

Answer 8

I get (x, y) = (ln3, 3)

Answer 9

f'(x) = 2e^x - 6 = 6 => 2e^x=12 => e^x = 6 => x = ln6

Answer 10

(ln6, 21-6ln6)

Answer 11

do you follow?

Answer 12

yes, that should be the correct one. Thanks!

Answer 13

do you understand how to do those?

Answer 14

I have to do more reading to understand it better how to find the y value

Answer 15

once you have the x that makes the slope you need, you just plug that into the original equation to find y.

y=f(ln6) = 9 +2e^(ln6)-6(ln6) => y=9+2(6)-6ln6=9+12-6ln6 = 21-6ln6