The equation f'(x) = 2x represents the derivative of a function f(x) . This means that the slope of the function at any point x is equal to 2x . As x increases, the slope also increases, indicating that the function is becoming steeper. To find the original function f(x) , we can integrate f'(x) . The integral of 2x is x^2 + C , where C is a constant. Thus, the function f(x) can be expressed as f(x) = x^2 + C , showing a parabolic shape.