Maximum of a cosine graph

Question

I am working on part b). I have determined, by graphing, that the maximum value is $4$ (at $x=0$, $y=4$; the max point is $0,4$)

Now, to find an expression for part b, I was trying to find the period of the function.

Using $p=(2\pi)/b$

$p = 14$

I'm not sure where to go from here. I know the maximum point will be reached again every $14$ units, so to speak. Any hints would be appreciated.

Answer 1

Let $x_{max}$ the values where the function reaches its maximum. Then,

$$\begin{array}{rcl} \text{max value: }4&=&6\cos\bigg(\frac{2\pi}{14}x_{max}\bigg)-2\\ 6&=&6\cos\bigg(\frac{2\pi}{14}x_{max}\bigg)\\ 1&=&\cos\bigg(\frac{2\pi}{14}x_{max}\bigg)\\ \Rightarrow 2k\pi&=&\frac{2\pi}{14}x_{max}\qquad k\in\mathbb{N}\\ \Rightarrow x_{max}&=&14k\qquad k\in\mathbb{N} \end{array}$$