Answer is done, 

The answer is done, but I just need a detailed step-by-step how to get there. I'm still confused. Please show me step-by-step.


First note that $f$ has to be continuous. Hence we should have 
\[\lim_{x\rightarrow 4^-}f(x)=\lim_{x\rightarrow 4^+}f(x)   \Rightarrow  c(4)^2=10-4d.\]
\[16c=10-4d.       (1)\]

For $x< 4$, we have
\[f'(x)=2cx    \Rightarrow  \lim_{x\rightarrow 4^-}f'(x)=2c(4)=8c.\]

For $x>4$ we have

\[f'(x)=-d    \Rightarrow  \lim_{x\rightarrow 4^+}f'(x)=-d.\]

For $f'$ to be continuous, we should have 

\[\lim_{x\rightarrow 4^-}f'(x)=\lim_{x\rightarrow 4^+}f'(x)   \Rightarrow  8c=-d.\]
\[8c=-d.     (2)\]
Solving the symstem of equations (1) and (2), we have
\[16c=10-4d,     16c=-2d \Rightarrow  10-4d=-2d\]
\[10=2d   \Rightarrow   d=5. \]
\[16c=-2(5)=-10. \Rightarrow c=-\frac{-10}{16}=-\frac{5}{8}.\]

The answer is accepted.
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