Parallel tangent lines

Question

anonymous · Answer

attachment

kinggeorge · Answer

Well, you need to take the derivative of both equations, and then set them equal to each other. In this case, you get $2x+5=e^x$. So you need to find any $x$ that satisfies that.

anonymous · Answer

I tried plugging that into the graphing calculator and got a weird decimal, could you show me how to do it algebraically?

kinggeorge · Answer

Since it's multiple choice, you can just try the different values and one of them should be very close to the answer. Algebraically, it's not pretty at all.

anonymous · Answer

ooh lol yea good idea

kinggeorge · Answer

Although if you graphed the two lines, you can also tell that there are two intersection points, and estimate what they are.

anonymous · Answer

to solve the equation ....well ...nuts !

anonymous · Answer

lol yea dont worry i got the right points with the intersections thanks

kinggeorge · Answer

It's almost like trying to integrate e^(x^2)!

anonymous · Answer

http://www.wolframalpha.com/input/?i=e%5Ex%3D2x%2B5

anonymous · Answer

{{x == (-5 - 2 ProductLog[-1\/(2 E^(5\/2))])\/2}, {x == (-5 - 2 ProductLog[-1, -1\/(2 E^(5\/2))])\/2}}

anonymous · Answer

ooo