To find the function f(x) when f'(x) = 3x + 7, we need to integrate the right-hand side of the equation.
Integrating both sides, we have:
β«f'(x) dx = β«(3x + 7) dx
Using the power rule of integration, we can integrate each term separately:
β«f'(x) dx = β«3x dx + β«7 dx
Integrating each term, we get:
f(x) = (3/2)x^2 + 7x + C
where C is the constant of integration.
So, the function f(x) is given by:
Answer: f(x) = (3/2)x^2 + 7x + C, where C is a constant.