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Once I've found the second derivative, I equate it to zero in order to determine concavity, but I don't know how to solve it after that

I'm just having a hard time solving with the ln or whatever you have to do..

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- Thread starter winston2020
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- #1

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Once I've found the second derivative, I equate it to zero in order to determine concavity, but I don't know how to solve it after that

I'm just having a hard time solving with the ln or whatever you have to do..

- #2

Hootenanny

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Are you trying to solve the equation to find t=*something*? Or are you tring to do something else? Is t a function of x? Could you clarify your problem please because at the moment it makes no sense whatsoever.

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- #3

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- #4

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(The function should have been f(t) not f(x))

- #5

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Plug the value of t you have (from setting 1st derivative = 0) into the 2nd derivative.

Is the result positive, negative, or zero?

- #6

Hootenanny

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Err, just one problem with that: ePlug the value of t you have (from setting 1st derivative = 0) into the 2nd derivative.

[tex] y(x) = e^x-x[/tex]

[tex]y^\prime(x) = e^x-1[/tex]

Hence, y(x) has a stationary point when,

[tex]e^x = 1 \Rightarrow x=0[/tex]

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- #7

HallsofIvy

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No, you don't "equate the second derivative to zero in order to determin concavity".

Once I've found the second derivative, I equate it to zero in order to determine concavity, but I don't know how to solve it after that

I'm just having a hard time solving with the ln or whatever you have to do..

The concavity of f(t)

The second derivative of e^(-9t) is 81e^(-9t) and , as pointed out by others, that is

- #8

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Thanks for all your help everyone

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