Final answer:
To determine the slope of the tangent to the function f(x) at x = -3, the derivative of the function is calculated, yielding f'(x) = 6x + 2, and then evaluated at x = -3, giving a slope of -16.
Step-by-step explanation:
To find the slope of the tangent to the curve f(x) = 3x^2 + 2x at the point where x = -3, we need to compute the derivative of the function f(x) which gives us the slope of the tangent at any point on the curve. The derivative of f(x) with respect to x, denoted as f'(x), is calculated by applying the power rule: f'(x) = d/dx (3x^2 + 2x) = 6x + 2. Substituting x = -3 into the derivative gives f'(-3) = 6(-3) + 2 = -18 + 2 = -16. Therefore, the slope of the tangent at x = -3 is -16.