The discussion revolves around finding the greatest and lowest values of the function \( y = x + \sqrt{x} \) over the interval [0, 4]. Participants are exploring the relationship between the function's critical points and its endpoints to determine these extrema.
Some guidance has been provided regarding evaluating the function at the endpoints and finding critical points. Participants are actively engaging with the concepts but have not reached a consensus on the specific steps or clarity of the explanation.
There is an emphasis on understanding the conditions under which maximum and minimum values occur for continuous functions on a closed interval, as well as the need for clarity in communication of the mathematical reasoning involved.
This is pretty vague, so you might understand what you mean, but you're not stating it clearly. What you need to do is to evaluate f(0) and f(4). Then you need to find f'(x) and set it to zero. If there is a number c for which f'(c) = 0, then evaluate f(c). Of the three numbers f(0), f(4), and f(c), one of them will be the largest function value on the interval [0, 4] and one will be the smallest.Penultimate said:Thanks that's gives a clue.
So i replace a and b in the function , then equals it to 0 and compare a ,b and c. Isnt it so?