# Thread: Derivative of some function f(x) at some number a

1. ## Derivative of some function f(x) at some number a

I have a limit question on my homework that I don't know how to do.
The limit represents the derivative of some function f(x) at some number a.

lim (tan(x) - 1) / ( x - (π/4))
x →π/4

I have to select all appropriate f(x) and a from a list that was given for the answer. The list was:

f(x) = tan(x), a = π/4
f(x) = tan(x), a = π
f(x) = tan(x) - 1, a = π
f(x) = tan(x), a = 1/4
f(x) = tan(x) - 1, a = 1/4
None of these

How would I solve this question? Thanks in advance.

2. Originally Posted by zer0e
I have a limit question on my homework that I don't know how to do.
The limit represents the derivative of some function f(x) at some number a.

lim (tan(x) - 1) / ( x - (π/4))
x →π/4

I have to select all appropriate f(x) and a from a list that was given for the answer. The list was:

f(x) = tan(x), a = π/4
f(x) = tan(x), a = π
f(x) = tan(x) - 1, a = π
f(x) = tan(x), a = 1/4
f(x) = tan(x) - 1, a = 1/4
None of these

How would I solve this question? Thanks in advance.
by knowing and understanding the definition of a derivative of a function at a specific x-value, say $x = a$ ...

$f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}
$