Question

For the given function, state the amplitude and the minimum output for the function.

Answer 1

Step-by-step explanation:

Let the following function:

`f(x)=A\cos(Bx\text{ -C})\text{ + D}`

by definition, the amplitude of this function is the absolute value of A.

Now, consider the following function:

`f(t)=3\cos((6)/(5)t)`

then, by definition, the amplitude of this function would be:

`|3|\text{ = 3}`

now, to find the minimum output of the given function we can use the first derivative criterion:

Notice that the critical points would be:

`t=(5\pi)/(3)n,\text{ t=}(5\pi)/(6)+(5\pi)/(3)n`

now, the domain of f(x) is:

`\text{ -}\infty\text{ < t <}\infty`

thus, the interval where the function is decreasing is:

`(5\pi)/(3)n\text{ < t < }(5\pi)/(6)+\text{ }(5\pi)/(3)n`

and the interval where the function is increasing is:

`(5\pi)/(6)+(5\pi)/(3)n\text{ < t < }(5\pi)/(3)n\text{ + }(5\pi)/(3)`

thus, we can conclude that the minimum output occurs when

`t=\text{ }(5\pi)/(6)+(5\pi)/(3)n`

and this output would be - 3.

Then, the correct answer is:

Answer: