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**[SOLVED] Finding the Max Value of a Function on a closed interval**

**1. Homework Statement**

Hi, I'm reposting this because it's a subsection to a larger question I had and I figured more people might be able to help with a new topic name.

anyway i have the equation (eq1) C(t) = C + a(e^.5t) + b(e^.9t) t>0 [3,12]

a,b and C are constants.

**3. The Attempt at a Solution**

I realized from long ago that the max and mins of a function occur when y'=0

So I took the derivative of the function which gave me

C(t) = Css + a(e^.5t) + b(e^.9t) t>0

c'(t)= .5a(e^.5t) + .9b(e^.9t) = 0

i took the ln of the whole thing

and that gave me

[ln(.5a)*.5t] + [ln(.9b)*.9t] = 0

my question now is can use the property that ln(xy) = ln(x)+ln(y) to combine the two ln's and thereby combining the coeffiecients of t such that it is .5t+.9t = .14t

and the whole thing would be .14t*ln(.45ab)= 0

....... that seems to be wrong considering that the t's cancel out but I can't think of much else...