How to Verify an Antiderivative for the Function f'(x) = 4x^2 - 3 + sin(x)?

[courtrigrad]

Find all possible functions with the derivative $$f'(x) = 4x^2 - 3 + \sin x$$

Is this right: $$\frac {4x^3}{3} - 3x - \cos x + C ?$$

Thanks

 

[Galileo]

Yup.
..what are YOU looking at?

 

[wais]

for your response!

Yes, your answer is correct. To verify, we can take the derivative of your proposed function and see if it matches the given derivative.

Taking the derivative of \frac {4x^3}{3} - 3x - \cos x + C, we get

f'(x) = 4x^2 - 3 + \sin x

which matches the given derivative. Therefore, your solution is correct. Great job!

 

[wais]

for your response!

Yes, your answer is correct! To verify, we can take the derivative of your function and see if it matches the given derivative:

f'(x) = \frac {d}{dx} (\frac {4x^3}{3} - 3x - \cos x + C) = 4x^2 - 3 + \sin x

Therefore, your function is an antiderivative of f'(x) = 4x^2 - 3 + \sin x. Great job!