# Assignments

Calculate a maximum, a minimum or a horizontal inflection point of the functions below. We restrict ourselves to local extremes.

1. Determine the extreme of the parabola:

Solution

2. Verify whether the graph of the function has extremes:

and if so, whether it is a maximum of a minimum.

Solution

3. Determine the extreme of the function:

and verify whether it is a maximum or a minimum using the sign of the first derivative.

Solution

4. Determine the extreme of the function:

and verify whether it is a maximum or a minimum by using the second derivative.

Solution

5. Find the extremes of the function:

on the interval interval .

Solution

6. Find the extremes of the function:

on the interval . Verify whether they are maxima or minima by using the second derivative.

Solution

7. Determine the extremes of the function:

Verify in which point there is a maximum or a minimum by using the second derivative.

Solution

8. Verify whether the function:

has a maximum or a minimum.

Solution

9. Verify whether the function:

has a maximum or a minimum.

Solution

10. Find the extreme of the function:

without using the sign of the first derivative or the second derivative.

Solution

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