# Simple differentiation (I think) Maximum problem? Basic calc.?

Find value of t @ which pt a is maximum? : p(t) (12*10^5)t^2(e^1000t)

Does that question make any sense? I don't understand what point a is? Is it just asking to find maximum? In which case I would just differentiate correct? Thanks.

Relevance

P(t)=(12*10^5)*t²*e^1000t

P'(t)=2(12*10^5)t*e^1000t+1000(12*10^5)t²*e^1000t

P'(t)=[(24*10^5)t*e^1000t](1+500t)

P'(t)=0 gives t=-1/500

I think t in this question should be time.

P''(t)=24*10^5*e^1000t*(5*10^5*t²+2000t+1)

P''(t)＜0 thus x=-1/500 gives a maximum

where y=24/5e²

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