Loser66
  • Loser66
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
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Loser66
  • Loser66
Options: 1) 10/e 2) 10 3) 10e 4) \(e^{10}\) 5) e brb
freckles
  • freckles
\[y=10x \\ \text{ means } y'=10 \text{ at some point } (m,n) \\ \text{ so we have the following } \\ n=10m \\ 10=be^{bm} \\ n=e^{bm} \\ \\ \text{ multiplying } n=e^{bm} \text{ on both sides by b gives us } bn=be^{bm} \\ \implies nb=10 \implies b=\frac{10}{n} \implies b=\frac{10}{10m}=\frac{1}{m} \\ \text{ going back to } n=e^{bm} \text{ we have} n=e \\ \text{ so } m=\frac{n}{10}=\frac{e}{10} \text{ and so } b=\frac{1}{m}\] one last thing to do and I leave it to you
freckles
  • freckles
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

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freckles
  • freckles
Not trying to imply they are easy just got bored testing myself :p
Loser66
  • Loser66
Thanks a lot. :)

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