Question

Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?

f(x), and the maximum is 3.

g(x), and the maximum is 5.’

f(x), and the maximum is 2.

g(x), and the maximum is 2.

Answer 1

Second option

g(x), and the maximum is 5.’

Explanation:

In the graph it can easily be seen that the maximum value reached by the function f(x) is y = 3.

Then, the function g (x) is:

`g(x) = 3cos((1)/(4)(x + (1)/(3)x)) + 2`

By definition the function

`y = cos(x)` reaches its maximum value when x = 0,
`2\pi`,
`4\pi`, ...,
`2k\pi`

So

When
`((1)/(4)(x + (1)/(3)x)) = 0` entonces
`cos(((1)/(4)(x + (1)/(3)x)) = 1`.

Thus:

`g(0) = 3(1) + 2\\\\g(0) = 5`.

Therefore the function that has the greatest maximum is g(x) when
`g(x) = 5`

The answer is the second option