Find using the defintion f '(c) lim = f(x) - f(c)

x -> c _______

x - c

the gradient function f ' (x) for:

a) f(x) = 1/x

b)f(x) =√ x

[My tutor told me to rationalize before doing the question for part b but how do i rationalize this]

- Jul 19th 2008, 07:58 AMsweetGFind using the definition........the gradient function f '(x)
**Find using the defintion f '(c) lim = f(x) - f(c)**

x -> c _______

x - c

the gradient function f ' (x) for:

a) f(x) = 1/x

b)f(x) =**√ x**

[My tutor told me to rationalize before doing the question for part b but how do i rationalize this]

- Jul 19th 2008, 08:15 AMflyingsquirrel
- Jul 20th 2008, 05:51 AMsweetG
Sorry I didn't realize that the definition for f '(c) was all over the place....sorry about that.

For Part b is the answer:

**(x-c)/(x****√x + x√c - c√x - c√c**and for Part (a) how am I supposed to find f '(x)

Sorry this question is really confusing me

coz there are so many x's and c's.......

- Jul 20th 2008, 06:40 AMflyingsquirrel
That's it but if you try computing you'll see that this limit is an indeterminate form. (both the numerator and the denominator tend to 0) If you hadn't expanded the numerator, it would have given you

And isn't an indeterminate form any longer. Can you find the value of this limit ?

Quote:

and for Part (a) how am I supposed to find f '(x)

Sorry this question is really confusing me

coz there are so many x's and c's.......

- Jul 20th 2008, 08:01 AMsweetG
Does f '(c) = 1/2√c

which therefore makes f ' (x) = 1/2√x

Is this right or have I made a mistake ? - Jul 20th 2008, 10:52 AMflyingsquirrel