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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.

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What do your notes/textbook say about local maxima and points of inflection? – Mark S. Nov 19 '12 at 1:03
points of inflection is when the second derivative equals 0, and the local maxima is when the first derivative equals DNE or 0 – John Lee Nov 19 '12 at 1:08
Have you taken the first and second derivative, and if so, what did you get? Please edit your post to include your work thus far, so we can better help you. – amWhy Nov 19 '12 at 1:10
up vote 2 down vote accepted

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.

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