values where f(x) = axe^(bx^2) has max f(2) = 1  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

values where f(x) = axe^(bx^2) has max f(2) = 1

Postby nona.m.nona on Fri Jan 30, 2009 2:30 am

For what values of the numbers and does the function have the maximum value



We've done the derivative tests.





Plug 2 in for x.





But if , then would be always zero.







Plug 2 in for x.



For the product to be less than zero (so the function is concave down giving a max), the factors have to have opposite signs.





But so

Back at the start:









Is that right? Thx.
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Postby stapel_eliz on Fri Jan 30, 2009 6:24 pm

You can always check your work:

. . . . .

Does (2, 1) lie on this curve?

. . . . .

Is there a critical point at x = 2?

. . . . .

. . . . .

. . . . . . . . ..

And is the second derivative negative at x = 2, so the curve is concave down, and the critical point represents a maximum?

. . . . .

. . . . .

. . . . . . . . . ..

It looks good to me! :thumb:

Eliz.
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