Final answer:
To find the value of df⁻¹/dx at the point x = 4, we need to find the derivative of the inverse function of f(x) = 7x³ - 13x² - 5, x ≥ 1.5.
Step-by-step explanation:
To find the value of df⁻¹/dx at the point x = 4, we need to find the derivative of the inverse function of f(x) = 7x³ - 13x² - 5, x ≥ 1.5. The inverse function can be found by switching x and y and solving for y. Let's call the inverse function g(x).
To find the derivative of g(x), we can use the chain rule. The chain rule states that the derivative of f(g(x)) with respect to x is equal to the derivative of f(g(x)) with respect to g(x), multiplied by the derivative of g(x) with respect to x.
Once we have the derivative of g(x), we can substitute x = 4 to find the value of df⁻¹/dx at that point.