Question

Question is attached in photo Function : f(x)=x+2 sin x

Answer 1

Answer:

The function is given below as

$f(x)=x+2\sin x$

Using the interval below

$0\leq x\leq2\pi$

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).

Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).

Using a graphing tool, we will have the relative maximum and relative minimum to be

Hence,

The relative maximum is at

$(\frac{2\pi}{3},3.826)$

The relative minimum is at

$(\frac{4\pi}{3},2.457)$