how do you estimate the instantaneous rate of change

Question

anonymous · Answer

first i made of tables of points that are getting closer and closer the point 
but im not sure what to do next

anonymous · Answer

if you are evaluating "instantaneous" rate of change, you'll evaluate your function as t (time) goes to zero, i think u need to use limits $$\lim_{t \rightarrow 0}(f(t)/t)$$

anonymous · Answer

so my equation is f(x)=(100x^2)/(t^(3)+5t^(2)-100x+380) and in want to know the instantaneous velocity at f(10) i would take the limit of that equation as x->10?

myininaya · Answer

$$f'(10) \text { \to find instaneous rate of change at x=10}$$

myininaya · Answer

you have x and t going on there
that is weird

anonymous · Answer

oh ya the t's are supposed to be x's

turingtest · Answer

Instantaneous rate for change is$$f'(x)=\lim_{\Delta x \rightarrow 0}{f(x+\Delta x)-f(x)\over\Delta x}$$so the estimation is the same formula with a finite sized Delta x; i.e. no limit$$f'(x)=\lim_{\Delta x \rightarrow 0}{f(x+\Delta x)-f(x)\over\Delta x}\approx{f(x+\Delta x)-f(x)\over\Delta x}$$for reasonably small Delta x. How small Delta x has to be for a good estimate depends of how curved the function is around the point in question.