Suppose $f(x)$ is a mystery function, where $f^{\prime \prime}(x)=8$ and $f^{\prime}(4)=6$. Then, $f^{\prime}(10)=$

Step 1 ：Suppose $f(x)$ is a mystery function, where $f^{\prime \prime}(x)=8$ and $f^{\prime}(4)=6$. The question is asking for the value of the derivative of the function at x=10.

Step 2 ：Since the second derivative is the derivative of the derivative, we can integrate the second derivative to find the derivative. The integral of a constant is a linear function, so the derivative of the function is a line with slope 8.

Step 3 ：We also know that the derivative at x=4 is 6. We can use this information to find the y-intercept of the line, and then use the equation of the line to find the derivative at x=10.

Step 4 ：Let's denote the derivative of the function as $f^{\prime}(x) = C + 8x$. We know that $f^{\prime}(4) = 6$, so we can solve for C.

Step 5 ：Substituting $f^{\prime}(4) = 6$ into the equation, we get $6 = C + 8*4$. Solving for C, we find that C = -26.

Step 6 ：Now we can substitute C = -26 into the equation $f^{\prime}(x) = C + 8x$ to get $f^{\prime}(x) = -26 + 8x$.

Step 7 ：Finally, we can substitute x = 10 into the equation to find $f^{\prime}(10) = -26 + 8*10 = 54$.

Step 8 ：So, the derivative of the function at x=10 is \(\boxed{54}\).