Thread: Antiderivative Word Problems
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Old December 1st, 2008, 07:54 PM
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Quote:
Originally Posted by helppalusmath View Post
2) f"(x) = -4sin(2x), f ' (0)= -4, f(0) = -6
Find f(pi/5)?

For this problem I keep getting sin2x- 4x -6, then solving: I'm not sure what I'm doing wrong, can you show me step by step for this one? Thanks.
f''(x) = -4sin(2x)
(Integrate & solve for C)
f'(x) = 2cos(2x) + C
(-4) = 2(1) + C
f'(x) = 2cos(2x) - 6
(Integrate & solve for C)
f(x) = sin(2x) - 6x + C
(-6) = (0) - 6(0) + C
f(x) = sin(2x) - 6x - 6

You probably made an error evaluating the constant for f'(x), which threw you off the trail for the rest of the problem, I believe. Evaluating the function should be a piece of cake after this.
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