# F'(x) = 2x(f(x)) and f(2) = 5, find

1. Feb 28, 2012

### LearninDaMath

f'(x) = 2x(f(x)) and f(2) = 5, find......

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

Suppose that f'(x) = (2x)(f(x)) and f(2) = 5

Find g'(∏/3) if g(x) = f(secx)

2. Relevant equations

no idea

3. The attempt at a solution

No idea where to begin but i'll give it a try...

nothing comes to mind...i don't know where to start...

before I attempt to solve, can anyone explain what this question even means? or point me in the direction to some online source that explains this...I would greatly appreciate it.

I never had a problem where there was a function of the form f(x) within a derivative function statement.

2. Feb 29, 2012

### Curious3141

Re: f'(x) = 2x(f(x)) and f(2) = 5, find......

If f(x) = y, f'(x) is another way of denoting dy/dx (the derivative).

Can you do the question now? The first part involves setting up a simple differential equation. Once you've found an expression for f(x), the second part just involves differentiating f(sec x) (using Chain Rule) and substituting pi/3 into the result.

3. Feb 29, 2012

### Fredrik

Staff Emeritus
Re: f'(x) = 2x(f(x)) and f(2) = 5, find......

You're asked to find g'(π/3). That's obviously the value of the function g' at π/3. So you need to find the function g', and then insert π/3 into it. You haven't been told what g' is, but you've been told that $g=f\circ\sec$. g' is the derivative of g, so the first step is obviously to find the derivative of g. Since g is a composition of two functions, you have to use the chain rule.

4. Feb 29, 2012

### LearninDaMath

Re: f'(x) = 2x(f(x)) and f(2) = 5, find......

Got it, thanks! Is there any useful application of a problem of this nature?

5. Feb 29, 2012

### Curious3141

Re: f'(x) = 2x(f(x)) and f(2) = 5, find......

Sorry about my previous post, I was at work and rushing and did not read the question carefully enough. There's a much simpler way to do the problem, as you've no doubt figured out with Fredrik's help. Of course, solving directly for f(x) will also give you the same answer, it's just a little more tedious.

This sort of problem is usually constructed "just so" in order to test your application of concepts. So sec(pi/3) here will equal to 2, which is why you're given f(2) in particular so that all the pieces fit well, and you can quickly arrive at a solution. In real life, it's not usual to find problems so neatly constructed.

6. Mar 1, 2012

### LearninDaMath

Re: f'(x) = 2x(f(x)) and f(2) = 5, find......

No prob at all, i'm always appreciative of the help given by you and others. Regarding you second paragraph, it's interesting that there seems to be (aside from the problems, like this one, meant to just test understanding of the computational concept) a slight disconnect between the physical representation and the graphical representation for the problems in the book. I continue to solve various derivative problems, but I would like to see what they mean if translated to some physical example. And visa versa, there are many physical problems in the book, such as the sliding ladder (that I recently posted), in which I am interested to see how that would be represented graphically.

Last edited: Mar 1, 2012