Calculus Grapher slides math.pdf - PhET

Given this function, talk with your groupabout what you think the derivative andintegral curves will look like and sketchF(x) ()

ZOOMEDintegral graphonlyanswer

Post lesson slides start here

What does the function of thisgraph look like?

Possible answers

What does TILT do?The derivative graph ZOOM was notThe derivative graph ZOOM was notchanged; the height changedbecause of increased slope.

What does the function of thisgraph look like?

Possible answers: Shift doesn’t matter again, and TILT changes valuesof derivative graphORThe derivative graph ZOOM was notchanged; the height changedbecause of increased slope.

Clicker questions for post‐lessonOpen Calculus Grapher andMoving Man before startingclicker questions

1. A car started from a stoplight,then sped up to a constant speed.This function graph describes his..A. PositionB. VelocityC. Acceleration

Use Moving man to show this: I set the acceleration at about 3then paused the sim by the time the man got to the 4 spot, thenI changed the acceleration to 0. If you have Moving man openwith this type of scenario, you can use the grey bar to show thatthe speed was zero increasing and then constant.

2. To find out howfar he traveled, youwould useA.IntegralB.FunctionC. Derivative

Use Moving Man Replay to showPosition is found dby the integralcurveDerivative curve shows acceleration

3. Your friend walks forward at a constant speedand then stops. Which graph matches her motion?A. Position curve B. Velocity curveC. Position curve D. Acceleration curveE. More than one of these

Use Moving man toshow this: I set theMan at about ‐6position, made thevelocity about 4, thenpaused the sim by thetime the man got tothe 4 spot, then Ichanged the velocityto 0. If you haveMoving man openwith this type ofscenario, you can usethe grey bar to help.

4. Which could be thederivative curve?AF(x)BC

Pedestal Linear ParabolaF(x)For each case, if the function, F(x) isvelocity, what could a possible story forthe motion of a person walking?

5. Three race cars have thesevelocity graphs. Which oneprobably wins?A B C D No wayto tell

Max valueUse integral totell that theparabolic onetraveledfarthest