Question

(Calculator Needed) The median size of a new single family house (in square
feet) built in the U.S. between 1987 and 2001 can be modeled as
h(x) = 0.359x3 - 15.198x2 + 221.738x + 826.514;
where x is the number of years since 1980.
Find all possible inflection points of h from 1987 to 2001 and determine whether it is actually
an inflection point

Answer 1

well you need to differentiate with respect to x

find the 1st derivative and let it equal zero and then solve for x. These are the stationary points.

next find the 2nd derivative

test the stationary points by substituting into the 2nd derivative,

if

y" > 0 you have a minimum at the stationary point

y" < 0 you have a maximum at the stationary point

y'' = 0 you have a horizontal point of inflection.

next let y'' = 0 and solve for x.

the solution may be a point of inflection but you need to check for a change in concavity

pick values on either side of the solution close to the solution and substitute them
into the 2nd derivative... look for a change in concavity... 1 should be > 0 and 1 < 0

hope this helps