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First order differential equations solving
Recent questions in Analyzing functions
Analyzing functions
asked 2021-03-04
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
asked 2021-02-11
\(\displaystyle{f{{\left(\theta\right)}}}={\sin{\theta}}{{\cos}^{{2}}\theta}-\frac{{{\cot{\theta}}}}{\theta}+{1}\)
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
asked 2021-02-02
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
asked 2021-01-08
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
asked 2020-12-24
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
asked 2020-11-26
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
asked 2020-11-23
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
asked 2020-11-08
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.
\(\displaystyle{f{{\left({x},{y}\right)}}}={\left({4}{x}-{1}\right)}^{{2}}+{\left({2}{y}+{4}\right)}^{{2}}+{1}\)
Analyzing functions
asked 2020-10-27
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.
\(\displaystyle{f{{\left({x},{y}\right)}}}=-{4}{x}^{{2}}+{8}{y}^{{2}}-{3}\)
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