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Investigation of the function. Extremum of the function. Convexity, concavity and point of inflection. Asymptotes
Theoretical questions:
1. L’Hospital’s Rule;
2. Monotonic conditions. Extremum of function;
3. Convexity and concavity. Point of inflection;
4. Аsymptotes;
5. Scheme of investigation of function and charting.
Classroom assignments:
1. Find the limits using L'Hospital's rule:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
2. Conduct a complete investigation of the functions and construct their graphs: 1. 
2. 
3. Describe the concavity of the graph of 
for 
.
4. Find 
and 
so that the function 
has a point of inflection at 
.
5. Find the domain and all asymptotes of the following function: 
.
6. Find the maximum and minimum values of 
on the interval [0, 5].
Homework:
Theoretical material: Functions of several variables and main properties. Partial derivatives and differentials.
Solve problems:
1. Find the limits using L'Hospital's rule:
1. 
2. 
3. 
4. 
2. Conduct a complete investigation of the functions and construct their graphs: 1. 
2. 
.
3. Find the domain and all asymptotes of the following function: 
.
4. Find the domain and all asymptotes of the following function: 
.
5. Find the maximum and minimum values of 
on the interval [-2, 1].
6. Find the maximum and minimum values of 
on the interval 
.
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