💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! # Find $f$.$f"'(x) = \cos x$, $\quad f(0) = 1$, $\quad f'(0) = 2$, $\quad f"(0) = 3$

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

Derivatives

Differentiation

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##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  Lectures

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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. California Baptist University

#### Topics

Derivatives

Differentiation

Volume

##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  Lectures

Join Bootcamp