Question

Can someone please help me understand how to solve the following:
f(x) = x^2, and f'(x) = 2x. Find a differential equation for f. For this example, it should be of the form f′(x) = f(x) ∗ g(x) where your task is to find
g(x).

Answer 1

you know f(x) = x^2 and f'(x) = 2x

therefore:

f'(x) = 2x = f(x) * g(x) = x^2 * g(x)

you should be able to work out what g(x) is from this

Answer 2

so g(x) would = 1, correct?

Answer 3

so you are saying that:

2x = x^2 * 1

?

Answer 4

I know this is rudimentary, but I'm embarrassed to say I dont know the answer.

Answer 5

what do you need to multiply x^2 by in order to make it equal to 2x?

Answer 6

another way to look at this is to write it as:\[2x=x^2\times g\]and you need to solve for g

Answer 7

do you know how to solve for g?

Answer 8

no, I don't.

Answer 9

ok - first divide both sides by \(x^2\) - what will you end up with?

Answer 10

I dont know

Answer 11

In that case you first need to brush up on algebra before you can tackle these types of problems. I would recommend http://www.khanacademy.org/

have a look there - it has many good tutorials on all types of subject areas.

Answer 12

Thanks asnaseer. I'm taking a statistics class right now, have completely forgotten algebra, and our prof has thrown us calculus question this week. I am completely lost! Ill brush up a bit! thanks for your help.

Answer 13

np - let me know if you require any further help.

BTW: the particular section section is: http://www.khanacademy.org/math/algebra