random anchor
Finding the instantaneous rate of change at t = 2hrs and t = 1hrs, the answer key for this past assignment gives 0 mph for t = 2hrs and 16mph for t = 1hrs, however for t = 1hrs I am only getting 12mph and for t = 2hrs I am getting 4 mph using the difference quotient f(x + h) − f(x)/h.
Using the same point f(x) and any different value for h should return the same instantaneous velocity, right?
remote depot
Finding the instantaneous rate of change at t = 2hrs and t = 1hrs, the answer ke...
No dude you want h to be super duper small like 0.00001
The smaller the h, the better the approximation for the “instantaneous rate of change”
random anchor
Oh actually? I had no idea, I've just been using arbitrary points
remote depot
Yeah
random anchor
That makes way more sense though thinking about it. So here we would just use the smallest points we can see on the graph?
remote depot
Wym
remote depot
Oh actually? I had no idea, I've just been using arbitrary points
You were probably thinking of the secant line
random anchor
Like for here at t(1hr) from the graph, without drawing a tangent line would I just use 1.125 as my next point?
remote depot
Here we’re trying to find the tangent line
random anchor
You were probably thinking of the secant line
Yes! That was it, for average rate of change right?
remote depot
Yeah
random anchor
This makes way more sense now
remote depot
Like for here at t(1hr) from the graph, without drawing a tangent line would I j...
You could do that but preferably something like 1 and 1.001
random anchor
I got 16mph using 1.125
random anchor
You could do that but preferably something like 1 and 1.001
For sure
Just based on the key
Thank you so much Daniel!
remote depot
Here I’ll link a desmos graph that shows why h needs to be small to get a tangent line. Play around with the h and p sliders
random anchor
Thank you again!