How Do You Calculate Instantaneous Rate of Change in an Electrical Circuit?

[ArielM]

Hi everyone, i am new to this website and i would like to ask one question that i don't quite get.
we have started a new topic in class about rates of change

Homework Statement

An Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.

a) find the average rate of change from 0.75 seconds to 1.5 second
b)find the instantanious rate of change at 1.5 second.
c)Identify any vertical asymptotes.

Homework Equations

The Attempt at a Solution

I have managed to solved part a by substituting the values 0.75 and 1.5 to the equation.
i then took both answers and found the average rate of change by the formula y2-y1/x2-x1 (correct me if I am wrong)

as for finding the instanatnious rate of change - i am completley clueless :(
Thanks in advance !

Ariel Melichovich

 

[tiny-tim]

Welcome to PF!

Hi Ariel! Welcome to PF!

n Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.
…
as for finding the instanatnious rate of change - i am completley clueless :(

Instantaneous rate of change is the derivative, dC/ds.

 

[ArielM]

Hi Ariel! Welcome to PF!


Instantaneous rate of change is the derivative, dC/ds.

Thank you for your reply !
however, i am not quite sure what does the term 'd' mean. is that the derivative?

can the form (x,x+h) be apllied to this question where at the end i divide the equation by "h"?

Thanks again !

 

[HallsofIvy]

If you do not know how to find a derivative, then you cannot do this problem. The derivative is the "instantaneous rate of change". But from what you say, you seem to have heard of the basics of the derivative: it is the limit, as h goes to 0, of the average rate of change from x to x+ h. However, for the rational function you have, that is going to be a difficult algebraic calculation.

Your calculation of the average rate of change is correct