Question

5. Determine the average rate of change of f(x)=6 cos(2x) – 4 on the interval [pi/4,pi]

Answer 1

Answer:

$- \frac{8}{\pi}$

Step-by-step explanation:

Use slope formula.

Rise over run.

Or

y over x.

$\frac{ {y}^{2} - y {}^{1} }{ {x}^{2} - x {}^{1} }$

Over changes in x value would be - 3/4 pi.

Plug in seepage intervals for x to find y.

$6 \cos(2(\pi) - 4$

In the regular function,

$\cos(\pi) = 1$

Since our period is 2, it would stay the same since 1x2=2

Since our amplitude is 6, our y value now is 6.

Since our vertical shift is -4, our y value is 2.

So

$6 \cos(2(\pi)) - 4 = 2$

${x}^{2} = \pi \: \: \: \: {y}^{2} = 2$

Let do the other point,

$\cos( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}$

Our period is 2 so

$\frac{ {\pi} }{4} \times \frac{2}{1} = \frac{\pi}{2}$

$\cos( \frac{\pi}{2} ) = 0$

Multiply this by 6.

It stays 0 then subtract 4 we get

$6 \cos(2( \frac{\pi}{4} )) - 4 = - 4$

Use the earlier formula, slope

$\frac{2 + 4}{ - \frac{3\pi}{4} } = - \frac{8}{\pi}$