Is my understanding of \"Derivative Function\" and \"Instantaneous Velocity\" co

Question

Is my understanding of "Derivative Function" and "Instantaneous Velocity" correct? Please make edits and look at the material with it!

1. The first is about the derivative function: http://www.calculusapplets.com/derivfunc.html

My Response:

While doing the first applet, Derivative Function, I noticed it is all about slope. You are able to find the average between two points, but what about when you need to find the slope at a single point? With the help of Calculus and its Applications with the applet I figured out with derivatives you use a small difference and have it shrink towards zero. By learning this fact and having knowledge of what the tangent line was, I was able to better understand what followed. Change in Y is equal to f (x+?x)

Explanation / Answer

1. I think you got the gist of it. Good

2. "From there we can relate it back to what we learned in the first applet"

Yes, because instantaneous velocity is just derivative, only that y represents the position and x represents time

"and then think of instantaneous velocity as the slope of the tangent line at a point on the curve like the average velocity of the secant line."

Yes, you can think as the slope of the tangent line at a point on a curve. But not like the average velocity of the secant line. It is the limit of the secant line when dx shrinks to 0 (here dt, where t is time), as already you mentioned in part A.

Obs: I did not look at applets, but used my knowledge

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.