The diagrams below are supposed to represent level sets for

The diagrams below are supposed to represent level sets for a function with isolated critical points. The heights of the levels are shown by the numbers around the edges. Some of the diagrams are incorrect, however. Indicate the ones that are correct by marking them T\' and the ones that are in error by marking them \"F\". (If a level\'s height is not marked, the diagram is considered correct if there exists a number that would work for that level.)

Solution

Picture 2. and 4. are true beacause there exists a isoated critical point that mean there exists a point where the derivative is zero and is the point isolatad means if i take a neighbourhood about this point there is no point other than this point.

On the other hand picture 1. has no isolated critical point and picture 3. had critical point which is not isolated.

So 1., 3. are F and 2., 4. are T