Question

For what value of b is the line y = 10x tangent to the curve \(y= e^{bx}\) at some point in the xy plane?
Please, help

Answer 1

Options:
1) 10/e
2) 10
3) 10e
4) \(e^{10}\)
5) e
brb

Answer 2

\[y=10x \\ \text{ means } y'=10 \text{ at some point } (m,n) \\ \text{ so we have the following } \\ n=10m \\ 10=be^{bm} \\ n=e^{bm} \\ \\ \text{ multiplying } n=e^{bm} \text{ on both sides by b gives us } bn=be^{bm} \\ \implies nb=10 \implies b=\frac{10}{n} \implies b=\frac{10}{10m}=\frac{1}{m} \\ \text{ going back to } n=e^{bm} \text{ we have} n=e \\ \text{ so } m=\frac{n}{10}=\frac{e}{10} \text{ and so } b=\frac{1}{m}\]
one last thing to do and I leave it to you

Answer 3

http://www.ets.org/gre/subject/about/content/mathematics
if anyone is curious these are gre practice questions
loser got me wanting to take this practice test buy I kind of got bored with them :p

Answer 4

Not trying to imply they are easy
just got bored testing myself :p

Answer 5

Thanks a lot. :)