## tangent lines

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

Fdonovan 3D
Posts: 101
Joined: Sat Aug 17, 2019 12:16 am

### tangent lines

Do we need to know how to find the slope of the tangent line to get an instantaneous rate?

Rhea Shah 2F
Posts: 97
Joined: Thu Jul 25, 2019 12:17 am

### Re: tangent lines

Yes, that's the easiest way to find the instantaneous rate for reactions. You could also just take the average rate over a very small time interval.

lauraxie2e
Posts: 108
Joined: Fri Aug 09, 2019 12:17 am

### Re: tangent lines

yes it is pretty easy though its just the derivative but also you could just find an average

205154661_Dis2J
Posts: 109
Joined: Wed Sep 18, 2019 12:21 am

### Re: tangent lines

You can just take the derivative to make it easier.

805394719
Posts: 104
Joined: Wed Sep 11, 2019 12:16 am

### Re: tangent lines

Yes. To find the slope of the tangent line you would have to either take a very small time step and divide the difference of the variables at those two time values and divide them by the time step. Another way to do it would be to take the limit of the difference of the variables at two times divided by the difference of the time which gives the average rate of change. Taking the limit as time goes to zero will minimize the time difference and give the instantaneous speed. This is also done by taking the derivative at that point if a function is given which is the same as taking the limit of the function.

Nare Nazaryan 1F
Posts: 101
Joined: Fri Aug 09, 2019 12:17 am

### Re: tangent lines

The slope of the tangent line is the same as the derivative, so you can just take the derivative.