Question

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

Answer 1

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:

$f(t)=3\cos(\frac{6}{5}t)$

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:

$t=\frac{5\pi}{3}n,\text{ t=}\frac{5\pi}{6}+\frac{5\pi}{3}n$

now, the domain of f(x) is:

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

thus, the interval where the function is decreasing is:

$\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{6}+\text{ }\frac{5\pi}{3}n$

and the interval where the function is increasing is:

$\frac{5\pi}{6}+\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{3}n\text{ + }\frac{5\pi}{3}$

thus, we can conclude that the minimum output occurs when

$t=\text{ }\frac{5\pi}{6}+\frac{5\pi}{3}n$

and this output would be - 3.

Then, the correct answer is:

Answer: