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May 23rd, 2010, 03:50 AM   #1
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Second Derivative Test

Let f(x) = (1 + x)^x

Use the Second Derivative Test to determine whether f has a local maximum or a local minimum at x = 0.

This question has gave me such a headache, as working out f''(x), is extremely long and I am thinking that there has to be some simple way to do it?
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May 23rd, 2010, 07:07 AM   #2
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Re: Second Derivative Test

I believe the first derivative is
Second derivative:

Sorry the exponents look weird, don't know how to use latex that well. They should be (x-1) or (x-2)

Or I guess you could use logarithmic differentiation.
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May 23rd, 2010, 07:24 AM   #3
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May 23rd, 2010, 07:50 AM   #4
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Re: Second Derivative Test

Quote:
Originally Posted by mathman2
. . .the exponents look weird . . .
3^{x\,+\,1} gives . Wrap the exponent in {}. The \, gives a bit of space between terms, signs etc.
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May 23rd, 2010, 08:19 AM   #5
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Re: Second Derivative Test

Oh, thanks a lot greg1313.
I had a feeling logarithmic differentiation would be more useful in this case.
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May 26th, 2010, 04:28 AM   #6
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Re: Second Derivative Test

there is first derivative test also
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