Question

describe the set of antiderivatives of f(x) = 1, where f is the derivative of f. choose the correct answer below. a. f(x)=x b. f(x)=x + c, where c is an arbitrary constant. c. f(x)=x^2 d. f(x)=cx, where c is an arbitrary constant.

Explanation:

Step1: Recall antiderivative formula

The antiderivative of a constant $k$ is $kx + C$, where $C$ is the constant of integration. Here $k = 1$.

Step2: Identify the antiderivative

The antiderivative of $f(x)=1$ is $F(x)=x + C$ since $\frac{d}{dx}(x + C)=\frac{d}{dx}(x)+\frac{d}{dx}(C)=1+0 = 1$.

Answer:

B. $F(x)=x + C$, where $C$ is an arbitrary constant.