1. Points A and B along a highway are 40km apart. Two cars pass point A at noon,

Question

1.

Points A and B along a highway are 40km apart. Two cars pass point A at noon, then pass point B at 12:30 P.M. Show that at some instant between 12:00 and 12:30, the two cars have the same velocity.

2.

Be sure to indicate local extrema and inflection points.

1. Points A and B along a highway are 40km apart. Two cars pass point A at noon, then pass point B at 12:30 P.M. Show that at some instant between 12:00 and 12:30, the two cars have the same velocity. 2. Use the guidelins to sketch the graph of the function f(x) = x^2e^{-x} Be sure to indicate local extrema and inflection points.

Explanation / Answer

the distance between A and B is 40 km/h

Suppose car 1 travels throughout at 40 km/h and car 2 travels for 1/2 hr at 30 km/h and 1/2 hr at 50 km/h

Suppose the first car overtakes the second at A, the second car will catch up exactly at B

Now look at the distance - time graph of the two cars.. NOWHERE WILL THE TWO SLOPES (WHICH REPRESENT VELOCITY) BE EQUAL

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