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Interval of concavity
- Thread starter Jtgs5249
- Start date
I'm having trouble with solving for the concavity.
F(x)=e^(2x) + e^(-x)
What I have tried is solving f'' for 0 and e^-1/2, If you need this, it must be typed with grouping symbols: e^(-1/2)
but my answer isn't matching the book.
Is this the right idea or is there something else I need to do?
Use either lower case or upper case. Here, if you use "F(x)," then you would use "F'(x)."
Write out what you got for F"(x). If you show us that, then we will have a starting
point so as to help you.
Last edited:
Bob Brown MSEE
Full Member
- Joined
- Oct 25, 2012
- Messages
- 598
What is important?
F(x), F'(x) and F''(x) are positive for all x.
By the way, if you share what the answer book says, then we can give you more information.
F(x), F'(x) and F''(x) are positive for all x.
By the way, if you share what the answer book says, then we can give you more information.
Bob Brown MSEE
Full Member
- Joined
- Oct 25, 2012
- Messages
- 598
Ok, great!
Answer: F''(x) is positive for all x.
Can you prove that to yourself?
Remember "all x"
You know that e^x > 0 for all x.
Answer: F''(x) is positive for all x.
Can you prove that to yourself?
Remember "all x"
You know that e^x > 0 for all x.
Last edited:
F(x), F'(x) and F''(x) are positive for all x.
No, that is true for F(x) and F''(x).
F'(x) = \(\displaystyle \ 2e^{2x} - e^{-x}.\)
When you solve F'(x) > 0, the solution is \(\displaystyle \ x \ > \ \dfrac{-ln(2)}{3}.\)
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