1. ## Differentiation

a wee bit stuck
Given f(x) = 5 + 7x – x^4, find f ' (x).
Use your result to find f ' (2)
im not sure what to do at all.

2. Originally Posted by Koops
a wee bit stuck
Given f(x) = 5 + 7x – x^4, find f ' (x).
there is a rule you must follow:

$\displaystyle \frac d{dx} x^n = nx^{n - 1}$

$\displaystyle \frac d{dx}$ means the derivative with respect to $\displaystyle x$

example:
$\displaystyle f(x) = x^3 + 2x^2 + 3x + 1$

$\displaystyle \Rightarrow f'(x) = 3x^2 + 4x + 3$

(did you see how the rule was applied?)

Use your result to find f ' (2)
im not sure what to do at all.
just plug in x = 2 once you have found $\displaystyle f ' (x)$

can you finish?

3. i knew the rule, it becomes, 7-4x^3
but what im unclear of is what f ' (x) means, and i dont know what to do to find it.

4. Originally Posted by Koops
i knew the rule, it becomes, 7-4x^3
but what im unclear of is what f ' (x) means, and i dont know what to do to find it.
what?? you found it! as you found, $\displaystyle f'(x) = 7 - 4x^3$

$\displaystyle f'(x)$ denotes the "derivative of $\displaystyle f(x)$"

5. oooooooooh i had a blonde moment
so now i just plug x=2 in