How to Find the Slope of a Cubic Graph

To find the slope of a cubic graph, you need to determine the derivative of the cubic function that represents the graph. A cubic function is typically expressed in the form:

f(x) = ax³ + bx² + cx + d

where a, b, c, and d are constants. The slope of the graph at any point is given by the first derivative of this function.

Here’s how to do it:

1. Differentiate the function: Take the derivative of f(x) with respect to x. Using basic differentiation rules, the derivative of the cubic function is:
2. f'(x) = 3ax² + 2bx + c
3. Evaluate the derivative at a specific point: If you want to find the slope at a particular point, substitute the x-coordinate of that point into the derivative. For example, to find the slope at x = x₀:
4. Slope (m) = f'(x₀) = 3a(x₀)² + 2b(x₀) + c

This value will give you the slope of the cubic graph at the specified point. In summary, finding the slope of a cubic graph involves taking the derivative of the cubic function and evaluating it at the desired x-coordinate.