Question

find the derivative of the given function at the indicated point (attached)

Answer 1

f(x) = 1/x, a = 2

Answer 2

i know i need to use \[\lim_{x \rightarrow a} \frac{ f(x)-f(a) }{ x-a }\]

Answer 3

f(x) = x^(-1), so f'(x) = -x^(-2). OK, just saw your last post and you have to do it from the definition of the derivative. I can help with that too.

Answer 4

You'd have to take the limit of [f(x + delta) - f(x)] / delta as delta goes to zero. That's a slightly easier way to do the problem.

Answer 5

[1/(x + delta) - 1/x] / delta = ( [x - (x + delta)] / x(x + delta) ) / delta = [-delta / x(x + delta)] / delta = -1/ x(x + delta). Now let delta go to 0. You get -1/(x^2)

Answer 6

So, the derivative at x=a is -1/(a^2). Is this making sense to you?