(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Finding the Max Value of a Function on a closed interval

1. The problem statement, all variables and given/known data

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...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the Max Value of a Function on a closed interval

**Physics Forums | Science Articles, Homework Help, Discussion**