The number of research articles in a prominent journal that were written by rese

Question

The number of research articles in a prominent journal that were written by researchers in Europe can be modeled by

P(t) = 7.0/ 1 + 5.4(1.2)t   where t is time in years. The graphs of P, P', and P'' are shown here. (Assume a = 4.)

Determine, to the nearest whole number, the values of t for which the graph of P is concave up, where it is concave down, and locate any points of inflection.

What does the point of inflection tell you about science articles?

From the graph of P' we see that P' has a maximum at around t =___________ , meaning that the number of articles written by researchers in Europe was increasing most rapidly at around t = __________.

I need help with all the blanks in this problem. I do not understand this at all. Thank you

concave up ________ < t < ____________ concave down _________ < t < ____________ point of inflection     t = _____________________

Explanation / Answer

Graph is concave up means P" > 0

So, using that here

Graph is concave up from t=0 to t=2.5a

And concave down from t = 2.5a to t=5a

And point of inflection is where P"=0

Means at t=2.5a

Inflection point tells 10 articles.

As P' > 0 for all t.

So, there is no maxima

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