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 thirddegree 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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 Fall '11
 Mr.Snickles
 Calculus, Derivative, FREERESPONSE SOLUTIONS, Skylight Publishing

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