Sketch the graph of a continuous function ƒ on [0, 4] satisfying the given properties.


ƒ' (x) and ƒ'3 are undefined; ƒ'(2) = 0; has a local maximum at x= 1; ƒ has local minimum at x = 2; and ƒ has an absolute maximum at x= 3; and ƒ has an absolute minimum at x = 4 .

Verified step by step guidance

1. Start by identifying the critical points based on the information given: ƒ'(2) = 0 indicates a local minimum at x = 2, and since ƒ' is undefined at x = 3, this suggests a potential local maximum or a point of inflection.
2. Plot the local maximum at x = 1, ensuring that the function increases to this point and then decreases afterwards, as it has a local minimum at x = 2.
3. At x = 2, draw the function so that it reaches a local minimum, meaning the graph should dip down to this point and then rise again towards x = 3.
4. At x = 3, since it is an absolute maximum, ensure that the function reaches its highest point here before decreasing towards x = 4, where it will have an absolute minimum.
5. Finally, sketch the graph to reflect that the function is continuous on the interval [0, 4], ensuring that it smoothly transitions through the identified points without any breaks or jumps.