The function $f(x)=2x^3-36x^2+210x-10$ has two critical numbers.
The smaller one is $x=$ and the larger one is $x=$

Step 1 ：The function given is $f(x)=2x^3-36x^2+210x-10$.

Step 2 ：The critical numbers of a function are the x-values where the derivative of the function is either zero or undefined. In this case, the function is a polynomial, so it will be defined for all x-values. Therefore, we only need to find where the derivative is zero.

Step 3 ：To find the critical numbers, we first find the derivative of the function. The derivative of $f(x)$ is $f^{\prime }(x)=6x^2-72x+210$.

Step 4 ：We then set the derivative equal to zero and solve for x. This gives us the critical numbers of the function, which are 5 and 7.

Step 5 ：Final Answer: The smaller critical number is $\boxed{{\displaystyle 5}}$ and the larger critical number is $\boxed{{\displaystyle 7}}$.