Hello,

I'm currently doing an bridging course and the people who I usually ask for help have time off for Christmas. As such I am hoping to get some assistance here.

I am having trouble working out the second derivative of the following

function: y=Ate^(-bt) with t being a variable, and A and B being unknown constants. The question I am solving is, "Verify the point of inflection occurs at t=2/b."

I have already found the

**first derivative** to be

A*(e^(-bt))-(bte^(-bt)), and assuming that is correct, I have worked out the following so far for the second derivative:

=A*(d/dt(e^(-bt)))-(b*(d/dt(t)*e^(-bt)))

=A*(e^(-bt)*(d/dt(-bt)))-(b*(d/dt(t)*e^(-bt))+(t*(d/dt(e^(-bt))))

=A*(-be^(-bt))-be^(-bt)+(t*e^(-bt)*(d/dt(-bt)))

After this point I am getting myself confused. I have been using

http://www.derivative-calculator.net...=2&showsteps=1 as a guide, but am having trouble figuring out why the (d/dt(t)) becomes a +1, instead of just being a multiplier in the third to last line.

Once I get this derivative worked out, I then need to solve to 0 to find the PoI.

Any help will be appreciated.

Thanks.

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