Final answer:
The derivative of the function g(x) = 8x² - 16x - 19 is found using the power rule, resulting in g'(x) = 16x - 16.
Step-by-step explanation:
The question pertains to the calculation of the derivative of the function g(x) = 8x² - 16x - 19. To find the derivative, we use basic differentiation rules. For the term 8x², we apply the power rule which states that the derivative of x^n is nx^(n - 1), thus producing 16x.
For the linear term -16x, the derivative is the coefficient -16 because the derivative of x is 1. The constant term -19 has a derivative of zero since the derivative of a constant is always zero. Therefore, the correct derivative is g'(x) = 16x - 16, confirming the student's expectation.