f'(x) = 3x^2 - 5cos(3x) + 90. Find f(x) and f''(x).

Finding f(x) requires integrating the function f'(x), because f(x) is the integral of the given function f'(x). So {integralsymbol} f'(x) dx = {integralsymbol} (3x^2 - 5cos(3x) + 90) dx = x^3 - (5/3)sin(3x) + 90x +Constant = f(x) Next differentiate f'(x) to get f''(x), because f''(x) is the derivative of f'(x). So f''(x) = d/dx (3x^2 - 5cos(3x) + 90). This is 6x+15sin(x).