# Recent questions in Analyzing functions

Analyzing functions

### Find and classify all the critical points for $$\displaystyle{f{{\left({x},{y}\right)}}}={3}{x}^{{2}}{y}-{y}^{{3}}-{3}{x}^{{2}}+{2}$$

Analyzing functions

### $$\displaystyle{f{{\left(\theta\right)}}}={\sin{\theta}}{{\cos}^{{2}}\theta}-\frac{{{\cot{\theta}}}}{\theta}+{1}$$ Domain: $$\displaystyle{\left[{0},{2}\pi\right]}$$ Find: 1) what are the inflection point 2) relationship of stationary point and critical point 3) what are the critical points

Analyzing functions

### Use the Second Derivative Test to classify the critical points of $$\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}+{2}{y}^{{2}}-{4}{x}+{4}{y}+{6}.$$

Analyzing functions

### Let f be a function whose Maclaurin series expansion. $$\displaystyle{f{{\left({x}\right)}}}={3}+{12}{x}+{24}{x}^{{2}}+{32}{x}^{{3}}+\ldots$$ Explain how you can determine f'(0), f''(0), and f'''(0) simply by analyzing the oefficients of x, $$\displaystyle{x}^{{2}}$$, and $$\displaystyle{x}^{{3}}$$ in the given representation and without directly alculating f'(x), f''(x), and f'''(x) from the representation above.

Analyzing functions

### Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points. $$\displaystyle{f{{\left({x},{y}\right)}}}={y}{e}^{{x}}-{e}^{{y}}$$

Analyzing functions

### Find the critical points of the following functions. Use the Second Derivative Test to determine whether each critical point corresponds to a loal maximum, local minimum, or saddle point. $$\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{4}}+{2}{y}^{{2}}-{4}{x}{y}$$

Analyzing functions

### For the graphs $$\displaystyle{x}={\left|{y}\right|}{\quad\text{and}\quad}{2}{x}=-{y}^{{{2}}}+{2}$$ (a) Sketch the enclosed region, showing all the intersection and boundary points. (b) Find the area of the enclosed region by integrating along the y-axis

Analyzing functions