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I have a few questions and I was wondering if someone could check my answers.

1) Given the velocity function http://texify.com/img/%5CLARGE%5C%21v%28t%29%20%3D-%28t%2B1%29%20%5Csin%7B%5Cfrac%7Bt%5E%7B2%7D%7D%7B2%7D%7D%20.gif ,[/URL] find all the times on hte open interval 0<t<3 where the particle changes direction. Justify your answer.

I said, the possible places where this occurs is when v=0. So I solved for v =0, and the only number that matches that domain is approximately 2.5 Are there any other answers I am missing? Is my idea of when the particle changes direction v=0 the entire reasoning to when the particle changes direction? I thought of an instance where v=0 but then particle doesn't change direction but rather keeps going in the same direction. Any help?

2)Suppose a function g is defined by http://texify.com/img/%5CLARGE%5C%21k%5Csqr%7Bx%2B1%7D%20%5C%20%5C%20%20for%20%5C%20%5C%200%5Cleq%20x%20%5Cleq%203%20%5C%5Cmx%2B2%20%5C%20%5C%20%20for%20%5C%20%5C%203%3C%20x%20%5Cleq%205%20.gif where k and m are constants. If g is differentiable at x=3, what are the values for k and m?

I was usually able to solve this but now there is one extra variable that I do not know how to get rid of. What do I do?

1) Given the velocity function http://texify.com/img/%5CLARGE%5C%21v%28t%29%20%3D-%28t%2B1%29%20%5Csin%7B%5Cfrac%7Bt%5E%7B2%7D%7D%7B2%7D%7D%20.gif ,[/URL] find all the times on hte open interval 0<t<3 where the particle changes direction. Justify your answer.

I said, the possible places where this occurs is when v=0. So I solved for v =0, and the only number that matches that domain is approximately 2.5 Are there any other answers I am missing? Is my idea of when the particle changes direction v=0 the entire reasoning to when the particle changes direction? I thought of an instance where v=0 but then particle doesn't change direction but rather keeps going in the same direction. Any help?

2)Suppose a function g is defined by http://texify.com/img/%5CLARGE%5C%21k%5Csqr%7Bx%2B1%7D%20%5C%20%5C%20%20for%20%5C%20%5C%200%5Cleq%20x%20%5Cleq%203%20%5C%5Cmx%2B2%20%5C%20%5C%20%20for%20%5C%20%5C%203%3C%20x%20%5Cleq%205%20.gif where k and m are constants. If g is differentiable at x=3, what are the values for k and m?

I was usually able to solve this but now there is one extra variable that I do not know how to get rid of. What do I do?

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