Final answer:
The slope of the tangent to the given curve at a point where x equals a is found by differentiating the function and substituting a for x in the derivative.
Step-by-step explanation:
To find the slope, m, of the tangent to the curve y = 8 - 5x² - 2x³ at the point where x = a, we need to take the derivative of the function to get the slope function. Taking the derivative, we get y' = -10x - 6x². Substituting x = a into the derivative gives us the slope of the tangent line at that point, m = -10a - 6a².