Max value of this function

[kaye]

Hi I'm out of training in math, I have to calculate the max value of this function:

$$f(x)=\bigg(1- \Big(\frac {acdx}{b(a+x)}\Big)\bigg)\bigg(\frac{acdx}{a+x}\bigg)-x$$
I somehow know I have to use the derivate, but I'm not sure how to proceed exactly. Thank you.

 

[Dr.Peterson]

Hi I'm out of training in math, I have to calculate the max value of this function:

$$f(x)=\bigg(1- \Big(\frac {acdx}{b(a+x)}\Big)\bigg)\bigg(\frac{acdx}{a+x}\bigg)-x$$
I somehow know I have to use the derivate, but I'm not sure how to proceed exactly. Thank you.

Have you tried finding the derivative? We'll want to see where, if at all, you have trouble doing so.

Then, you will want to set that equal to zero and solve, if possible.

It will also be helpful if you can tell us the context of the problem. Do you have to solve it for an application at work, or as homework, or something else? That will affect how we choose to help.

In other words:

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[Cubist]

Hi, welcome to FMH !

I agree with @Dr.Peterson that the context is important, and did you post the whole thing?

I can see from inspection (without taking a derivative) that if b<0 and acd>0 then there isn't a maximum and f(x) can become arbitrarily large.