find the following formula
a curve of the form y = e^(-(x-a)^2/b) b>0
local max: x=32
inflection points: x=36 x=28
find a and b
im not sure how to use the values given to find a and b...any help
$\displaystyle y=e^{-\frac{(x-a)^2}{b}}$
Find the 1st derivative and set it equal to zero to find max/mins.
$\displaystyle y'=e^{-\frac{(x-a)^2}{b}} \frac{2x-2a}{b}$
$\displaystyle 0=-e^{-\frac{(32-a)^2}{b}} \frac{2(32)-2a}{b}$
You have one equation, two unknowns. To find inflection points, set the 2nd derivative equal to zero.
$\displaystyle y''=-e^{-\frac{(x-a)^2}{b}} \left(\frac{2x-2a}{b}\right)^2 -e^{-\frac{(x-a)^2}{b}} \frac{2}{b} $
$\displaystyle 0=-e^{-\frac{(x-a)^2}{b}} \left(\frac{2x-2a}{b}\right)^2 -e^{-\frac{(x-a)^2}{b}} \frac{2}{b} $
Plug in for x = 36 and x = 28 and you have three equations with two unknowns. Happy solving!