Difference between revisions of "009A Sample Final 2, Problem 10"
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::<math>f(x)=\frac{4x}{x^2+1}</math> | ::<math>f(x)=\frac{4x}{x^2+1}</math> | ||
| − | <span class="exam">(a) Find all local maximum and local minimum values of <math>f,</math> find all intervals where <math>f</math> is increasing and all intervals where <math>f</math> is decreasing. | + | <span class="exam">(a) Find all local maximum and local minimum values of <math style="vertical-align: -4px">f,</math> find all intervals where <math style="vertical-align: -4px">f</math> is increasing and all intervals where <math style="vertical-align: -4px">f</math> is decreasing. |
| − | <span class="exam">(b) Find all inflection points of the function <math>f,</math> find all intervals where the function <math>f</math> is concave upward and all intervals where <math>f</math> is concave downward. | + | <span class="exam">(b) Find all inflection points of the function <math style="vertical-align: -4px">f,</math> find all intervals where the function <math style="vertical-align: -4px">f</math> is concave upward and all intervals where <math style="vertical-align: -4px">f</math> is concave downward. |
| − | <span class="exam">(c) Find all horizontal asymptotes of the graph <math>y=f(x).</math> | + | <span class="exam">(c) Find all horizontal asymptotes of the graph <math style="vertical-align: -5px">y=f(x).</math> |
| − | <span class="exam">(d) Sketch the graph of <math>y=f(x).</math> | + | <span class="exam">(d) Sketch the graph of <math style="vertical-align: -5px">y=f(x).</math> |
| + | <hr> | ||
| + | [[009A Sample Final 2, Problem 10 Solution|'''<u>Solution</u>''']] | ||
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| + | [[009A Sample Final 2, Problem 10 Detailed Solution|'''<u>Detailed Solution</u>''']] | ||
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[[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']] | [[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']] | ||
Latest revision as of 10:29, 1 December 2017
Let
(a) Find all local maximum and local minimum values of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f,} find all intervals where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is increasing and all intervals where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is decreasing.
(b) Find all inflection points of the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f,} find all intervals where the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is concave upward and all intervals where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is concave downward.
(c) Find all horizontal asymptotes of the graph Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(x).}
(d) Sketch the graph of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(x).}