Given the graph,
goo.gl/photos/VTMjKvNsVvAQwe3X6
a) What is the slope of the tangent line to the graph of f^-1 at the point (-1/2,-1)?
b) What is the slope of the tangent line to the graph of f^-1 at the point (1,2)?
a) 2
b) 1/2
correct
To find the slope of the tangent line to the graph of f^-1 at a given point, we can use the derivative. However, since we're working with the inverse function, we need to apply a special property.
a) To find the slope of the tangent line to the graph of f^-1 at the point (-1/2, -1), we need to find the derivative of f at the point (-1, -1/2).
To start, you'll need to find the derivative of f(x). Since we don't have the equation or definition of the function f(x) from the given graph, we'll work with an estimation based on the graph.
Take two points on the graph near (-1/2, -1) and calculate their slope to estimate the slope of the function at that point. You can choose two points on the curve that are close enough to (-1/2, -1) but on either side of it. Remember that the slope of the tangent line is equivalent to the derivative of the function evaluated at a point.
b) Similarly, to find the slope of the tangent line to the graph of f^-1 at the point (1, 2), we need to find the derivative of f at the point (2, 1). Again, since we don't have the equation or definition of the function, use the same estimation method as in the previous question. Select two points near (1, 2) that are on either side of it and calculate their slope.
By estimating the slope using this method, you can get an approximate value for the slope of the tangent line to the graph of f^-1 at each given point.