Question

Graph the function f(x)=x+3−−−−√3. What are the minimum and maximum values on the interval [−11, 5]?

Answer 1

The minimum and maximum values of the function
`\( f(x) = x + 3 - √(3)\)`on the interval [-11, 5] are as follows:

- Minimum value: f(-11)

- Maximum value: f(5)

To find the minimum and maximum values of the function on the given interval, we need to evaluate the function at the critical points and endpoints within that interval.

1. **Endpoints:**

- Evaluate f(-11) and f(-11) to find the function values at the interval endpoints.

2. **Critical Points:**

- Find the critical points by setting the derivative of f(x) equal to zero and solving for x.

- Differentiate
`\( f(x) = x + 3 - √(3) \)` with respect to x.

- Set the derivative equal to zero and solve for x .

3. **Evaluate at Critical Points:**

- Evaluate f(x) \) at the critical points found in step 2.

4. **Compare Values:**

- Compare the function values at the critical points and endpoints to determine the minimum and maximum values on the given interval