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# Find $f$.$f"'(x) = 12 + \sin t$

## $2 t^{3}+\cos t+\frac{c t^{2}}{2}+y t+d$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

this problem here were given the second derivative F double prime of X. So we're wanting to find the correct answer of F. So we have F double prime of X. is equal to 12 plus. Um Scientific. Yeah. And this is going to be actually the triple crime after crime attacks. So then based on this, when we take F double prime attacks, that's an equal 12 X plus um minus coats and X. Are saying X. What's called accents on the team And Crime of act is going to equal 12 X squared over two cents. Six X squared. Okay. Um minus cynics. And this is gonna be plus C. So this will be plus C. X plus D. And lastly, ffx is going to end up giving giving us six X. Cubed over three. So that's two X cube minus Synnex is going to give us plus cosign axe, class Co sign or pussy x squared over two plus the eggs. Class E. And that would be our final answer. We can choose whatever constant values we want to. Um But this will be the final answer.

California Baptist University

#### Topics

Derivatives

Differentiation

Volume

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp