Question

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

Answer 1

`- (8)/(\pi)`

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( (\pi)/(4) ) = ( √(2) )/(2)`

Our period is 2 so

`\frac{ {\pi} }{4} * (2)/(1) = (\pi)/(2)`

`\cos( (\pi)/(2) ) = 0`

Multiply this by 6.

It stays 0 then subtract 4 we get

`6 \cos(2( (\pi)/(4) )) - 4 = - 4`

Use the earlier formula, slope

`(2 + 4)/( - (3\pi)/(4) ) = - (8)/(\pi)`