Question

# In this exercise, you will need to use a graphing utility to confirm your result.$f(x)=\sin x-\sqrt{3} \cos x$

Solution

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This task aims to visualize the monotonic aspect of a certain function, its critical points and its local extrema to confirm the results found in the previous parts of this exercise according to the given information.

In this exercise, we will plot the graph of the function $f$, identify the intervals on which $f$ is decreasing or increasing and interpret graphically the local extrema of the function.

Analytically, the function $f$ has two critical numbers at $x=\pi/6$ and $x=7\pi/6$, it is decreasing over $\left(\frac{\pi}{6},\frac{7\pi}{6}\right)$ and increasing over $\left(0,\frac{\pi}{6}\right)$ and $\left(\frac{7\pi}{6},2\pi\right)$, has a local maximum at $x=\pi/6$ and has a local minimum at $x=7\pi/6$.

Are there graphical properties of function graphs that we could use to our advantage to confirm the analytical results with the use of the plotted graph?