Find the intervals on which the graph of $f$ is concave upward, the intervals on which the graph of $f$ is concave downward, and the inflection points. \[ f(x)=-x^{4}+28 x^{3}-28 x+3 \]

Step 1 ：Given the function \(f(x)=-x^{4}+28 x^{3}-28 x+3\), we need to find the intervals on which the graph of \(f\) is concave upward, the intervals on which the graph of \(f\) is concave downward, and the inflection points.

Step 2 ：To find the intervals of concavity and the inflection points, we first need to find the second derivative of the function. The second derivative tells us where the function is concave up (where the second derivative is positive) and where it is concave down (where the second derivative is negative). The inflection points are where the second derivative is equal to zero or undefined.

Step 3 ：The second derivative of the function is \(-12x^2 + 168x\).

Step 4 ：The critical points, where the second derivative is equal to zero, are \(x = 0\) and \(x = 14\).

Step 5 ：Testing an interval around these points, we find that the function is concave up on the interval \((0, 14)\).

Step 6 ：\(\boxed{\text{Final Answer: The function } f(x)=-x^{4}+28 x^{3}-28 x+3 \text{ is concave upward on the interval } (0, 14) \text{ and the inflection points are at } x = 0 \text{ and } x = 14.}\)