
Math Help  Vertical Speed  Use Tangent Line Slope of Graph  Score Report 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, LCRD2 to LCRD4, 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(xp)^{2}+q is stated as dy/dx = 2a(xp) = slope of the tangent line. For example, the rate of change of the curve y = 4(x3)^{2}+6 is stated as dy/dx = 2(4)(x3). At a point P on this curve, say where x=1, the speed = derivative = dy/dx = 2(4)(13) = 16.  The score report automatically appears after you have made 10 choices.  The Math score is based on your choices only and does not count the butterfly hits.  The Game score is reduced by the number of butterfly hits.  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.  Refresh/Reload the webpage to start over again. 
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