The math help thread

I can try to help if what you're looking for is explanation.

[COLOR="Magenta"]Here's a problem I just can't figure out. I've got to find the following
a) derivative (straight forward, and easy)[/COLOR]
the rate of a function changing (f(x) changes as x changes)

[COLOR="Magenta"]b) minimum points
c) maximum points[/COLOR]
These 2 points are the spots where your graph changes direction. To put more simply: once something hits its top, it starts to decline and vice-versa. Imagine: going up, hitting A (maximum point #1), starts to go down, hits B (minimum point #1), starts to go back up, goes OVER A and may or may not hit C (maximum point #2.)
That's why A, B and C are called local maximum/minimum, they're the highest (or lowest) since on both sides the function graph is beneath (or above them.) These are points where the graph "bends"
So if you look at this, you'll see that when the graph "bends", the tangent line literally lies horizontally, suggesting that the first derivative is 0.

[COLOR="Magenta"]d) increasing
e) decreasing[/COLOR]
if x > xo and f(x) > f(xo) or if x < xo and f(x) < xo => increasing
otherwise, decreasing.

I think this part compares the way your function changes in comparison to the way your variable changes. If your x is increasing (x > xo) but your graph is going down (y < yo)
then the function is "growing" in the opposite direction of your variable's growth. Not really sure here.

f) second derivative (again straight forward)
Describes the changes of the tangent line (which is ... changing)

I'm not so sure about this myself lol.

[COLOR="Magenta"]g) concave up
h) concave down[/COLOR]
In the same gif image above, you see how the tangent line changes from "spinning" clockwise to counter-clockwise. The direction in which it "spins" determines its concavity. To make long stories short: mountain = concave down, valley = concave up. Why? The algebraic value of your tangent line continuously decreases on the concave down curve (hence why it's -down-) and vice-versa.

i) points of inflection
No idea. I only learned that this is where the graph changes from being concave up to concave down.

Tried my almost-best. Hope I helped.