AP Calculus AB
4.1/4.2 Learning Check (with review)
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 
2.
3.
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2
4.
5.
6.
The velocity of a particle moving along a horizontal axis is given by the function v  t   t 2  sin  2t 
1
for 0  t  5 . If the position of the particle at t  0 is , find an expression for the position of the
3
particle at any time t.
Find the absolute extrema of