Question

how do you find the instantaneous rate of change give f(x)=-1/x with the given point (1,2)

Answer 1

Instantaneous rate of change is another name for the derivative.
f'(x) = 1/(x^2).

I have a question though: @Teebhawj are you sure that is the correct point? It doesn't satisfy f(x) or am I missing something?

Answer 2

those are correct endpoints [1,2]

Answer 3

i found the average rate of change to be 1/2

Answer 4

I'm afraid I don't know what you mean. Are you looking for the point whose instantaneous rate of change is equal to the average rate of change?

Answer 5

how would you do the derivative of f(x)=-1/x

Answer 6

I am given the function and the endpoint and Im suppose to find the average rate of change and compare it to the instantaneous rate of change

Answer 7

There are two ways of looking at it: either the power rule or the quotient rule.
f(x) = -1/x = -1(x^-1) which utilizes the power rule. Or you can use the quotient rule.

To clarify, your point is (1,2) and your interval is x = 1 to x = 2?

Answer 8

I have just figured it out lol. I had to take the derivative of -1/x which = 1/x^2 and plug in the endpoints