Calculus
posted by Angel on .
The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation
D(t)=10.61t^(3)+208.808t^(2)168.202t+9775.234 donors, where t is the number of years after 1975. Find the inflection point(s) from t=0 through t=17 , if any exist.
a. There are no inflection points from t=0 through t=17 .
b. There is one inflection point at t=6.56.
c. There are inflection points at t=0 and t=17.
d. There is one inflection point at t=0.15.
e. There are inflection points at t=0, t=0.15,and t=17.
I thought it was B.

An inflection point is a point on a curve at which the second derivative changes sign. You must find point where second derivative = 0
Go on:
wolframalpha dot com
When page be open in rectangle type:
second derivative of 10.61t^(3)+208.808t^(2)168.202t+9775.234
and click option =
When you see result click option:
Show steps
Then in rectangle type:
solve 417.61663.66t=0
Inflection point is:
t=6.5601 
Thanks, i thought it was B. your awesome.