Provide an appropriate response.Graph f(x) = cos-1 x together with its first derivative. Comment on the behavior of f and the shape of its graph in relation to the signs and values of f'.

Question

What will be an ideal response?

Answer 1

The graph of f(x) = cos-1 x has negative slope on its domain [-1, 1]. Therefore all values of the first derivative are below the x-axis. The graph of f(x) becomes gradually less steep as the graph of f' approaches its vertex at x = 0. To the right of the y-axis, the graph of f' quickly descends and f(x) becomes more steep.