Practice question · Select all that apply
Select every function below that is an antiderivative of f(x) = 2x.
Hints
- Differentiate each candidate and see which ones return 2x.
- More than one answer is correct, which is the whole point of the constant.
Show the answer
- A. x^2 - 3
- D. x^2
- E. x^2 + 7
Why
x^2, x^2 + 7 and x^2 - 3 all differentiate to 2x, differing only by a vertical shift. The constant 2 differentiates to 0, and x^3/3 differentiates to x^2, that last one is the result of integrating 2x with the wrong rule applied twice.
Practise Integration and Antiderivatives
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