thats... thats how all functions work user.
Don't worry though, calculus has a way of making you forget earlier things.
How do we save math education?
Gabriel Reyes
Justin James
Fix teachers first, I don't know how it is in other regions, but in Ontario primary school and middle school teachers have zero math education requirements. You can't expect someone to teach math decently if they haven't done it since grade 11, until teaching education is reformed math education will be stagnant.
Landon Clark
It's not a troll.
Jose Hughes
No no user, people here are unironically autistic enough to think like this
Jackson Ross
Imagine you want to know the average change between two points of a curve, lets say the curve [math]f(x) = x^2[/math]. The slope between the points [math]a[/math] and [math]b[/math] would be if [math]b>a[/math] [math]\frac{f(b) - f(a)}{b - a}[/math].
Now you want to know the slope at a specific point of the curve to do this you make the interval smaller [math]\frac{f(x+h) - f(x)}{x + h - x}[/math] where [math]h[/math] is a small number say maybe 0.01. The limit is when a number goes closer towards a number so we take [math]\lim_{h \to_ 0} \frac{f(x+h) - f(x)}{x + h - x} = \frac{(x+h)^2 - x^2}{h} = \frac{x^2 + 2xh + h^2 - x^2}{h} = 2x + h = 2x[/math] and now we have the function for [math]f'(x)=2x[/math]
Charles Thompson
Just understand said courses (as well as their applications) really well.
Unfortunately, and especially with calculus, many teachers have no other answer to "why?" than "that's what The Rule says". In order to teach well, you need an intuitive mastery (NOT rote memorization) of the topic you intend to teach.
William Foster
If you need an intuitive understanding of calculus, check out this playlist: youtube.com
Aaron Morgan
sorry, I think I meant this: youtube.com
David Lewis
f'(2) just means the slope of f(x) at x = 2.
and f'(x) = 2x by the power rule
Jordan Rivera
Well, that's what my intention was. I tutored math at the trades school I went to (barely high school level stuff) and I'd always look up proofs for all the algebra and trig related stuff we'd do. That way I could tell students where the formulae for the volume or surface area of a sphere came from, etc.