Final answer:
The slope of the line tangent to the function f(x) = -x² + 4 at x = -3 is found by taking the derivative of the function and evaluating it at x = -3, resulting in a slope of 6.
Step-by-step explanation:
The slope of the line tangent to the function f(x) = -x² + 4 at x = -3 can be found by taking the derivative of the function and evaluating it at the point of interest. To find the derivative f'(x), we apply the power rule which states that the derivative of x^n is nx^(n-1). In our case, f(x) = -x² + 4, the power rule gives us f'(x) = -2x. Substituting x = -3 into f'(x) gives us f'(-3) = -2(-3) = 6. Therefore, the slope of the tangent line at x = -3 is 6.