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Numerade Educator

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Problem 48 Hard Difficulty

Find $ f $.

$ f"'(x) = \cos x $, $ \quad f(0) = 1 $, $ \quad f'(0) = 2 $, $ \quad f"(0) = 3 $

Answer

$$
f(x)=-\sin x+\frac{3}{2} x^{2}+3 x+1
$$

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Video Transcript

So here we give inevitable prima backs and our goal is to find um affects so after the prime of X co sign X double prime of X is going to equal Synnex because we know the derivative syntax is close in X. A rap class C the constant um is going to be F of F double prime of zero. We know is equal to three. That means C is equal to three. We have us I'm of X. He's going to give us negative cosign X. Because negative co 10 X derivative is syntax plus three X plus under constant. When that equals zero. We get to that means that the the here it's going to be three as a result. So an F crime or fx he's gonna give us a negative syntax class rehabs X squared plus three X. And then we have our final constant with initial conditions. That's one. And that is our final answer.