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July 31, 2014

July 31, 2014

Posted by **Carly** on Monday, July 11, 2011 at 11:33pm.

g(t)= (t^3/2)(e^-2t) for 0<t<1.

- Another Calculus -
**Reiny**, Tuesday, July 12, 2011 at 7:55amUsing the product rule

g'(t) = t^(3/2)(-2)e^(-2t) + (3/2)t^(1/2)(e^(-2t))

common factor ...

= (1/2)e^(-2t)(t^(1/2)) [-4t + 3}

set this equal to zero

from the first factor we get t=0

and from the second one we get t = 3/4

now evaluate

g(0) = ..

g(3/4) = ..

g(1) = ...

and determine which is the largest and smallest value.

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