# Homework Help: The greatest and lower value of the function in this segment.

1. Jun 18, 2009

### Penultimate

What is the greatest and lower value of the function$$y=x+\sqrt{x}$$
in the segment [0,4]?
I knowit has to do with deriving it , but i dont know how to explain it.
Any help :D

2. Jun 18, 2009

### qntty

The maximum and minimum of a continuous function f on [a,b] can only be in at a, b or a number c which satisfies f'(c)=0.

3. Jun 18, 2009

### Penultimate

Thanks thats 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?

4. Jun 18, 2009

### qntty

yes that's correct.

5. Jun 19, 2009

### Staff: Mentor

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.