- #1
intenzxboi
- 98
- 0
Homework Statement
Suppose that f has an inverse and f (6) = 18, f'(6) = 4/5. If g = 1/(f-1), what is g'(18)?
have no idea how to set up problem
The derivative of an inverse function is the slope of the tangent line at a given point on the inverse function's graph. It represents the rate of change of the original function at that point.
To find the derivative of an inverse function g, you can use the formula:
g'(x) = 1 / f'(g(x)), where f'(x) is the derivative of the original function f(x).
The derivative of a function and its inverse are reciprocals of each other. This means that if the derivative of f(x) is g'(x), then the derivative of g(x) is 1/g'(x).
Yes, the derivative of an inverse function can be negative. This can happen when the original function is decreasing at a certain point, resulting in a negative slope for the inverse function at that point.
Finding the derivative of an inverse function is important because it allows us to calculate the rate of change of the original function at a specific point. This is useful in many real-life applications, such as optimization problems and physics calculations.