$K$ Find the average value of the function $f(x)=x^{2}-17$ on $[0,6]$. The average value of the function $f(x)=x^{2}-17$ on $[0,6]$ is $\square$.

Step 1 ：Let's find the average value of the function \(f(x)=x^{2}-17\) on the interval \([0,6]\).

Step 2 ：The average value of a function \(f(x)\) on the interval \([a,b]\) is given by the formula \(\frac{1}{b-a}\int_{a}^{b}f(x)dx\).

Step 3 ：Substituting \(f(x)=x^{2}-17\), \(a=0\), and \(b=6\) into the formula, we get \(\frac{1}{6-0}\int_{0}^{6}(x^{2}-17)dx\).

Step 4 ：Evaluating the integral, we find that the average value of the function \(f(x)=x^{2}-17\) on \([0,6]\) is -5.

Step 5 ：Final Answer: \(\boxed{-5}\)