Curve Sketching Part 3 Youtube We demonstrate how to use calculus techniques to sketch cubic curves. In this video i continue going over examples using the guidelines to curve sketching and this time the function i graph is: y = x*e^xdownload the notes in my.
Curve Sketching Part 3 Youtube Math 111, dr. bahaaeldin, psu drive.google file d 14rdul3mbcaggsm7xppjqhywfkft746jb view?usp=sharing. Using the checklist above, we can sketch a curve while identifying the critical characteristics and components along the way. step by step example. for example, suppose we are asked to analyze and sketch the graph of the function. \begin{equation} f(x)= \frac{1}{3} x^{3} x \frac{2}{3} \end{equation} function analysis. Step 2. find the y intercept. the y intercept of a function f ( x) is the point where the graph crosses the y axis. this is easy to find. simply plug in 0. the y intercept is: (0, f ( 0 )). step 3. find the x intercept (s) an x intercept of a function f ( x) is any point where the graph crosses the x axis. This property is called the asymptote. an asymptote is a line that the curve gets very very close to but never intersect. there are three types of asymptotes: vertical, horizontal, and oblique. in this post, we discuss the vertical and horizontal asymptotes. in the graph above, the vertical and the horizontal asymptotes are the y and x axes.
Curve Sketching Part 3 Of 4 Youtube Step 2. find the y intercept. the y intercept of a function f ( x) is the point where the graph crosses the y axis. this is easy to find. simply plug in 0. the y intercept is: (0, f ( 0 )). step 3. find the x intercept (s) an x intercept of a function f ( x) is any point where the graph crosses the x axis. This property is called the asymptote. an asymptote is a line that the curve gets very very close to but never intersect. there are three types of asymptotes: vertical, horizontal, and oblique. in this post, we discuss the vertical and horizontal asymptotes. in the graph above, the vertical and the horizontal asymptotes are the y and x axes. A function can increase between two points in different ways, as shown in figure [fig:concav3]. in each case in the above figure the function is increasing, so that \(f'(x) > 0\), but the manner in which the function increases is determined by its concavity, that is, by the sign of the second derivative \(f''(x)\). Key idea 4: curve sketching. to produce an accurate sketch a given function \(f\), consider the following steps. find the domain of \(f\). generally, we assume that the domain is the entire real line then find restrictions, such as where a denominator is 0 or where negatives appear under the radical. find the critical values of \(f\).
Guidelines For Curve Sketching Part 1 Youtube A function can increase between two points in different ways, as shown in figure [fig:concav3]. in each case in the above figure the function is increasing, so that \(f'(x) > 0\), but the manner in which the function increases is determined by its concavity, that is, by the sign of the second derivative \(f''(x)\). Key idea 4: curve sketching. to produce an accurate sketch a given function \(f\), consider the following steps. find the domain of \(f\). generally, we assume that the domain is the entire real line then find restrictions, such as where a denominator is 0 or where negatives appear under the radical. find the critical values of \(f\).
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