Math Help - Vertical Speed - Use Tangent Line Slope of Graph - Game Tips:
- Method 1: Speed is equal to Distance divided by Time.
The vertical speed at point P is equal to the slope of the line tangent to the curve at point P.
Use any 2 points on the tangent line to find its slope = rise/run = (change in height)/(change in time).
Previous games, L-CRD2 to L-CRD4, demonstrate using 2 points on a line to find slope.
- Method 2: In Calculus, there is a derivative rule that calculates speed = instantaneous rate of change.
The derivative of the curve y = a(x-p)2+q is stated as dy/dx = 2a(x-p) = slope of the tangent line.
For example, the rate of change of the curve y = -4(x-3)2+6 is stated as dy/dx = 2(-4)(x-3).
At a point P on this curve, say where x=1, the speed = derivative = dy/dx = 2(-4)(1-3) = 16.
- The game can be played using the mouse by itself or using the keyboard by itself.
- If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus.
- Adjust the game's speed by pressing the + or - key repeatedly.