Professor never covered anything like this on his lecture notes, which tbh is rather infuriating. I know how to do linear approximation but not when it’s giving me two points and asking for a slope.
#Linear approximation, need a little guidance
dusky coral
chilly vigilBOT
royal geode
The definition of a derivative at the point a is:
$f'(a) = lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$
What this means is that we can take h very small (close to zero) to approximate f'(a).
If you take $h = 0.2$
Then you could write:
$f'(7.7) \approx \frac{f(7.7+0.2) - f(7.7)}{0.2}$
modest driftBOT
Daddy_314
dusky coral
Let me give it a try
So I’m confused, if in your example I’m using f(7.7), why am I being given f(7.9)?
royal geode
Re-read carefully
you are using both f(7.7+h) and f(7.7)
With h=0.2
So you need both
royal geode
yes
In fact f'(7.7) is almost the slope between the points
A( 7.7 ; f(7.7))
And B(7.9 ; f(7.9))
The closer we take B
The closer we can get to f'(7.7)
Here we took B far away from A by a step of h = 0.2
But we can take h smaller and smaller
dusky coral
Hmmm, lemme try it with a few others
What if you’re subtracting two different values? Like in here
dusky coral
Elaborate, please
royal geode
We have seen a formula above
In this chat
You need to rewrite it
And try to adapt it
To this exercise
The same formula
What is the function f here ?
What point a should we select ?
What is the value of the step h ?
dusky coral
That’s another confusing thing, when do we know what to select as point a
It feels like it’s just arbitrarily selected and I don’t know what it’s supposed to represent