Help Understand Calculus Word Problem

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kss

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I cant seem to figure out what to do with this problem.

The percentage of Southern Australia grasshopper eggs that hatch as a function of temperature (for temperatures between 7 degrees C and 25 degrees C) can be modeled by

P(t) = -0.0065t^4+0.488t^3-12.991t^2+136.560t-395.154, percent where T is the temperature in degrees C.

a) Graph P, P', P".
b) Find the point of most rapid decrease on the graph of P. INTERPRET your answer by INTERPRETING the relevant point on each graph.

I found P,P',P'' and graphed each one. I don't not understand what it means by find the most rapid decrease on the graph P and then interpret it.

P= -0.0065t^4 + 0.488t^3 - 12.991t^2 + 136.560t - 395.154
P'= -0.0258t^3 + 1.464t^2 - 25.982t + 136.56
P''= -0.0774^2 + 2.928T - 25.982
 
kss said:
I cant seem to figure out what to do with this problem.

The percentage of Southern Australia grasshopper eggs that hatch as a function of temperature (for temperatures between 7 degrees C and 25 degrees C) can be modeled by

P(t) = -0.0065t^4+0.488t^3-12.991t^2+136.560t-395.154, percent where T is the temperature in degrees C.

a) Graph P, P', P".
b) Find the point of most rapid decrease on the graph of P. INTERPRET your answer by INTERPRETING the relevant point on each graph.

I found P,P',P'' and graphed each one. I don't not understand what it means by find the most rapid decrease on the graph P and then interpret it.

P= -0.0065t^4 + 0.488t^3 - 12.991t^2 + 136.560t - 395.154
P'= -0.0258t^3 + 1.464t^2 - 25.982t + 136.56
P''= -0.0774^2 + 2.928T - 25.982
Click to expand...

For most rapid decrease (change) - which of those three (P, P' & P") need to be maximized/minimized?
 
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