By determining $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$, find $f^{\prime}(4)$ for the given function. \[ f(x)=2 x^{2} \]

Step 1 ：The given function is a simple quadratic function. The derivative of a function at a point gives the slope of the tangent line at that point. The derivative of a function can be found using the limit definition of the derivative, which is given in the question. We can substitute the function and the point into the limit definition to find the derivative at that point.

Step 2 ：Let's find the derivative of the function \(f(x)=2 x^{2}\).

Step 3 ：The derivative of the function is \(f^{\prime}(x) = 4x\).

Step 4 ：Substitute \(x = 4\) into the derivative function to find the derivative at that point.

Step 5 ：The derivative of the function at the point \(x=4\) is \(f^{\prime}(4) = 16\).

Step 6 ：Final Answer: The derivative of the function \(f(x)=2 x^{2}\) at the point \(x=4\) is \(\boxed{16}\).