Determine the Average Rate of Change

[eleventhxhour]

Determine the average rate if change of the function y = 2cos(x - $\pi$/3) + 1 for the interval $\pi$/3 $\le$ x $\le$ $\pi$/2

I tried finding the exact values of the two (0 and 0.5) and subbing them into the AROC equation but I keep getting the wrong answer (1.4)

 

[MarkFL]

We find:

$$\frac{\Delta y}{\Delta x}=\frac{y\left(\dfrac{\pi}{2}\right)-y\left(\dfrac{\pi}{3}\right)}{\dfrac{\pi}{2}-\dfrac{\pi}{3}}=\frac{\left(2\cos\left(\dfrac{\pi}{6}\right)+1\right)-\left(2\cos\left(0\right)+1\right)}{\dfrac{\pi}{6}}=\frac{6\left(\sqrt{3}-1\right)}{\pi}\approx1.39811405542801$$

 

[eleventhxhour]

We find:

$$\frac{\Delta y}{\Delta x}=\frac{y\left(\dfrac{\pi}{2}\right)-y\left(\dfrac{\pi}{3}\right)}{\dfrac{\pi}{2}-\dfrac{\pi}{3}}=\frac{\left(2\cos\left(\dfrac{\pi}{6}\right)+1\right)-\left(2\cos\left(0\right)+1\right)}{\dfrac{\pi}{6}}=\frac{6\left(\sqrt{3}-1\right)}{\pi}\approx1.39811405542801$$

Okay, that's what I got. The textbook has it as -0.5157 so I guess it's just wrong?

 

[MarkFL]

We both made an error...it should be:

$$\frac{\Delta y}{\Delta x}=\frac{6\left(\sqrt{3}-2\right)}{\pi}\approx-0.511745261674736$$

I discovered my error when graphing the function and the resulting secant line:

View attachment 3547