Is there a math concept that never made sense to you? Which one or ones do you wish someone would explain in new ways?
If none of these come close you can mention something as a comment.
@futurebird Before I read down the thread I didn’t know what ‘the derivitive’ even related to :D My father was an engineer, and obnoxious about Being Right, so I went into visual art where the criticism couldn’t follow.
After he died I went back to school for Comp Sci and had to study up to place out of the intro math class — I like math now, but have still never taken a class more advanced than Algebra II (back in 1977 that was)
@jacquiharper @futurebird Recently I've been casually trying to get a handle on what basic calculus is actually doing.
The derivative is the slope of the graph of a function at a given point. People talk about "rates of change" and "tangents", but no, it's a slope.
Exactly. A “rate of change” is a slope. 20miles/hour is a line with slope 20/1 because, for each 1 hour you go forward in the x-direction, your total total distance goes up by 20 miles in the y-direction.
A tangent is a straight line … again with a slope. So “the slope of a curve at a point” (curves being precisely those lines with non-consonant slopes) we use the tangent to define it in a way so that our straight-line idea of slope works.
@futurebird @Infrapink @jacquiharper
20mph isn't a rate of change; it's a velocity, unchanging.
32 feet per second squared is a rate of change, an accelearation.
A tangent is not a straight line.
https://mathbooks.unl.edu/PreCalculus/tangent-and-cofunctions.html
@phaedral @futurebird @Infrapink @jacquiharper
1/2
When traveling 20 miles per hour, your position is changing at the rate of 20 miles per hour. That's a rate of change in your position. A rate of change in position is the first derivative of position, also known as velocity. Velocity, in turn, also has its own first derivative, called acceleration, which is also the second derivative of position.
@llewelly @futurebird @Infrapink @jacquiharper I think when I read "rate of change" I assume the topic is "rate of change of the curve." However, that assumption was proved wrong by OP. Yes, 20mph is "a" rate of change. It is not, however a rate-of-change-of-a-curve, which is one of the mathematical questions I think calculus was invented to answer...the absurdity of "change over zero time."