APcal 2004-Solutions

# D f 4 c 4 2 for some 0 c 2 therefore 4 64 f

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Unformatted text preview: ( x) has a relative maximum at x = 2. (c) f (0) ≈ T (0) = 7 − 9 ( −2 ) − 3 ( −2 ) = −5 . We do not have enough information to 2 3 determine whether x = 0 is a critical number for f ( x) . For example, the whole family of functions g ( x) = T ( x) + C ( x − 2 ) , where C is any constant, has the same 4 third-degree Taylor polynomial T ( x) . f ( x) could be any one of these functions. One of these functions has a critical number at x = 0 — when 2 3 g ′(0) = −18 ⋅ ( −2 ) − 3 ⋅ 3 ( −2 ) + 4C ( −2 ) = 0 — others don’t. (d) f (4) ( c ) 4 ( −2 ) for some 0 ≤ c ≤ 2 . Therefore, 4! 64 f (0) − (...
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## This note was uploaded on 07/07/2013 for the course MATH AP taught by Professor Mr.snickles during the Fall '11 term at Benjamin N Cardozo High School.

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