Given the following table, give the best estimate for $f^{\prime}(9)-f(9)$ \[ \begin{array}{ccccccc} x & 0 & 3 & 6 & 9 & 12 & 15 \\ f(x) & 35 & 45 & 54 & 61 & 29 & 7 \end{array} \] The estimate is (Round your answer to the nearest tenth.)

Step 1 ：Given the following table, give the best estimate for \(f^{\prime}(9)-f(9)\)

Step 2 ：\[\begin{array}{ccccccc}x & 0 & 3 & 6 & 9 & 12 & 15 \\f(x) & 35 & 45 & 54 & 61 & 29 & 7\end{array}\]

Step 3 ：To estimate \(f^{\prime}(9)\), we can use the difference quotient formula, which is \(\frac{f(x+h)-f(x)}{h}\), where \(h\) is a small number. In this case, we can use the points \(x=6\) and \(x=12\) to estimate \(f^{\prime}(9)\), so \(h=3\).

Step 4 ：Then, we can calculate \(f^{\prime}(9)-f(9)\).

Step 5 ：\(f^{\prime}(9) = -8.333333333333334\)

Step 6 ：\(f(9) = 61\)

Step 7 ：\(f^{\prime}(9)-f(9) = -69.33333333333333\)

Step 8 ：Round your answer to the nearest tenth.

Step 9 ：Final Answer: The best estimate for \(f^{\prime}(9)-f(9)\) is \(\boxed{-69.3}\).