14. Given $f(x)=-10|x-4|+1$, use the definition of the derivative to find $f^{\prime}(4)$.
$-10$
0
10
Does not exist

Step 1 ：Given $f(x)=-10|x-4|+1$, we are asked to find $f^{\prime}(4)$.

Step 2 ：The derivative of a function at a point gives us the slope of the tangent line at that point.

Step 3 ：However, for absolute value functions, the derivative at the point where the function changes direction (in this case, x=4) does not exist because the function is not differentiable at that point.

Step 4 ：The slope of the tangent line is not defined because the function has a sharp turn at that point.

Step 5 ：Therefore, the derivative of the function f(x) at x=4 does not exist.

Step 6 ：Final Answer: \(\boxed{\text{Does not exist}}\)