Find a formula for a curve of the form
$y = \text{exp}\;\left(\frac{-(x-a)^2}{b}\right),\quad b>0,$
with a local maximum at $x=-3$ and points of inflection at $x=-7$ and $x=1$.
Help please guys I've been trying to figure this out for 30 minutes.
Find a formula for a curve of the form
$y = \text{exp}\;\left(\frac{-(x-a)^2}{b}\right),\quad b>0,$
with a local maximum at $x=-3$ and points of inflection at $x=-7$ and $x=1$.
Help please guys I've been trying to figure this out for 30 minutes.
Hint: By the Chain Rule, $\frac{dy}{dx}=-\frac{2(x-a)}{b}\exp\left(-\frac{(x-a)^2}{b}\right).$ This should be $0$ at $x=-3$. That will let you evaluate $a$ easily.
Now it's your turn for the rest. You will need the second derivative. Use the already calculated first derivative, and the Product Rule.