Question

analyze and sketch a graph of the function over the given interval. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.

Answer 1

Given the following function:

`f(x)=-x+2cos\text{ }x`

We will graph the function over the following interval

`0\leq x\leq2\pi`

The given function is the result of adding two functions

the first is the line y = -x

The second the trigonometric function y = 2cos (x)

the graph of the function will be as follows:

From the graph, we can find the following:

The y-intercept = (0, 2)

The x-intercept = (1.03, 0)

The local minimum = (7π/6, -5.397)