AP Calculus AB
Lessons 5-1 & 5-2 Learning Check (with review)
Name__________________________________
Date ________________________________
1. Determine if the Mean Value Theorem applies to f  x   2  x2 on the interval 0, 2  . If so, which of
the following points (x-value only) is guaranteed to exists by the MVT?
(A) No, the Mean Value Theorem does not apply.
(B) Yes; x  
2
2
2
(C) Yes; x  
1
2
(D) Yes; x 
1
2
2.
3.
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4.
5. The velocity of a particle moving along a horizontal axis is given by the function v  t   t 2  sin  2t  for
1
0  t  5 . If the position of the particle at t  0 is , find an expression for the position of the particle at
3
any time t.
6. Find the absolute extrema of
[-3, 2].