What is the Prime Function of f(x)=3x²+4 with verification

The prime function of a function refers to its derivative, which represents the rate of change of the function with respect to the independent variable (in this case, x). To find the prime function of f(x) = 3x^2 + 4, you need to calculate its derivative. In your case, f(x) = 3x^2 + 4, and both terms are constants, so the derivative is calculated as follows: f'(x) = d/dx [3x^2] + d/dx [4] Using the power rule: f'(x) = 2 * 3x^(2-1) + 0 f'(x) = 6x So, the prime function of f(x) = 3x^2 + 4 is f'(x) = 6x. Verification: To verify that f'(x) = 6x is indeed the prime function, you can take the derivative of f(x) with respect to x and check if it matches f'(x): f'(x) = 6x Now, take the derivative of f(x) = 3x^2 + 4 with respect to x: f'(x) = d/dx [3x^2] + d/dx [4] Using the power rule: f'(x) = 2 * 3x^(2-1) + 0 f'(x) = 6x As you can see, the derivative of f(x) is indeed 6x, which matches the prime function f'(x). This verifies that the prime function of f(x) = 3x^2 + 4 is f'(x) = 6x.