Quick Calc 1 problem (Antiderivative)

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SUMMARY

The discussion centers on finding the function f given its second derivative f'' and two initial conditions. The user derived the first derivative as f'(x) = 5x^4 + 4x^3 + 4x + C but struggled to progress due to the lack of clarity on the initial conditions. A solution was provided, indicating that by antidifferentiating f' to obtain f(x) and applying the conditions f(0) = 2 and f(1) = 1, the constants C and D can be determined through a system of equations.

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btbam91
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Hello, I'm looking for f given f'' and two conditions.

[PLAIN]http://img375.imageshack.us/img375/2572/antider.jpg

Going from f'' to f', I get f'(x) = 5x^4 + 4x^3 + 4x + C

But with the two conditions, I feel that I cannot progress from here. I feel that one of those conditions should be f'.


Any help is appreciated. Thanks.
 
Last edited by a moderator:
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btbam91 said:
Hello, I'm looking for f given f'' and two conditions.

[PLAIN]http://img375.imageshack.us/img375/2572/antider.jpg

Going from f'' to f', I get f'(x) = 5x^4 + 4x^3 + 4x + C

But with the two conditions, I feel that I cannot progress from here. I feel that one of those conditions should be f'.


Any help is appreciated. Thanks.
Antidifferentiate one more time to get f(x). You'll get another constant of integration, say D. Using f(0) = 2 and f(1) = 1, you'll have two equations in two unknowns, so you should be able to solve for C and D.
 
Last edited by a moderator:

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