Let $\displaystyle f(x) = \begin{cases} 0\quad & \text{for}\ \ 0 < x < 1, \\ -\left(4-x\right)\quad & \text{for}\ \ 1 < x < 4. \end{cases}$

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$\bullet\quad$ Compute the Fourier cosine coefficients for $f(x)$.

• $A_0 =$
  
  
• $A_n =$

$\bullet\quad$ Give values for the Fourier cosine series $\displaystyle C(x) = \frac{A_0}{2} \, + \, \sum_{n=1}^\infty A_n\,\cos\left(\frac{n\pi}{4}\,x\right)$.

• $\phantom{-}C(1) =$
  
  
• $C(-2) =$
  
  
• $\phantom{-}C(5) =$