Which of the following functions is an antiderivative of satisfying ?

Question

Which of the following functions  is an antiderivative of      satisfying ?

BlackTom AI · Accepted Answer

The question as provided is incomplete: it asks for an antiderivative of some function, but the original function to integrate (the integrand) is not stated, and the list of answer options is empty. This makes it impossible to determine which candidate is correct from the given data alone.

In a typical antiderivative problem, you look for a function F(x) such that F'(x) equals the given integrand f(x). If a candidate is F(x) = e^x + 2x + 4, you can check by differentiation: F'(x) = (e^x) + 2 + 0 = e^x + 2. Therefore, this candidate would be an antiderivative of the function f(x) = e^x + 2, up to an arbitrary constant (the constant 4 here is just one possible value for the constant of integration).

However, without knowing the actual integrand or the other options to compare, we cannot conclusively determine whether this candidate is a correct antiderivative in the intended context. If the integrand were e^x + 2, then any antiderivative would have the form e^x + 2x + C, and e^x + 2x + 4 would be one such antiderivative with C = 4. If the integrand were different, the derivative of this candidate would not match it, and the candidate would be incorrect.

Summary of key checks you would perform once the integrand is known:
- Differentiate the candidate F(x) and see if F'(x) equals the given integrand f(x).
- If the problem allows any constant of integration, recognize that F(x) = something + C is acceptable, so the specific constant (e.g., +4) is not essential to correctness.
- Compare against other provided options to identify which one yields the correct derivative.

Because the necessary information (the integrand and the answer choices) is missing, no definitive evaluation can be made here beyond describing the general method and demonstrating how F(x) = e^x + 2x + 4 would relate to a potential f(x) = e^x + 2.

MATH_1225_17255_202501 4.9 Antiderivatives

Which of the following functions is an antiderivative of satisfying ?

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