Final answer:
The slope of the tangent line to the function f(x) = 7x - 4x² at (-2,-30) is 23.
Step-by-step explanation:
The slope of a tangent line to a curve at a given point is equal to the derivative of the function at that point. To find the slope of the tangent line to the equation f(x) = 7x - 4x² at the point (-2,-30), we need to take the derivative of the equation and evaluate it at x = -2. The derivative of the function is f'(x) = 7 - 8x. Plugging in x = -2 gives us f'(-2) = 7 - 8(-2) = 7 + 16 = 23. Therefore, the slope of the tangent line is 23.