Mariam A.

asked • 03/30/22

Can you help me with this question?

Find the formula for a function of the form C(x) = e^{-(x-a)^2/b} for b>0 with (i) a local maximum at x=-5 and (ii) points of inflection at x=-8 and x=-2.

C(x) = ....................

Douglas B.

Nope. That is incorrect. There is a global maximum at x = a.
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03/30/22

Mariam A.

Can you explain to me how can we solve this problem?
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03/30/22

Doug C.

Mariam, I will add some explanation to my answer soon.
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03/31/22

1 Expert Answer

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Doug C. answered • 03/30/22

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Here are some hints.

Find C'(x), remembering that a and b are constants. C'(x) = 0 when, x = -5. Turns out this will let you find the value of a.

Easiest to find the 2nd derivative if you replace a with its value determined in previous step. Find C''(x), using the product rule.

C''(x) = 0 when x = -8 (or -2). This allows you to solve for b.

My thinking is that it will be easier to find derivatives if you rewrite C(x) as:


C(x) = e(-x^2+2ax-a^2)/b, although that is not necessary. Also remember that C(x) itself will never equal zero (e raised to any power is always positive).


If you still need help, post a comment.


desmos.com/calculator/dbnqnwxvii


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