Intervals of increasing/decreasing and concavity

[samantha0417]

f(x)= (1/x^3) + (2/x^2) + (1/x)

find intervals of increasing and decreasing and the intervals concavity. intercepts, asymptotes, inflections pts. and cusps and tangents need to be determined as well.

 

[tkhunny]

Have fun with that.

Have you considered a Common Denominator?

 

[stapel]

[F]ind [the] intervals of increas[e] and decreas[e] and the intervals [of?] concavity. [The] intercepts, asymptotes, inflections pts. and cusps and tangents need to be determined as well.

Finding the intercepts is something you learned back in algebra. How far have you gotten? Where are you stuck?

To find the asymptotes, use algebra to convert the sum of fractions to a common denominator, and rewrite the expression as one fraction. Then apply the rules you learned back in algebra regarding horizontal and vertical asymptotes. How far have you gotten? Where are you stuck?

Please clarify what you mean by "cusps". Which "tangents" are you needing to find?

To find the intervals of increase and decrease, apply what you've learned about the first derivative. To determine concavity, apply what you've learned about the second derivative. How far have you gotten? Where are you stuck?

Please be specific. Thank you.

Eliz.

 

[samantha0417]

how do you get a common dem.?

 

[stapel]

[H]ow do you get a common [denominator]?

Find the least common multiple, and convert each fraction to it. For instance:

. . . . .\(\displaystyle \L \frac{1}{2}\, + \,\frac{2}{5}\, = \left(\frac{1}{2}\right)\left(\frac{5}{5}\right)\, +\, \left(\frac{2}{5}\right)\left(\frac{2}{2}\right)\, =\, \frac{2}{10}\, +\, \frac{4}{10}\, =\, \frac{6}{10}\, =\, \frac{3}{5}\)

. . . . .\(\displaystyle \L \frac{1}{x\, +\, 2}\, +\, \frac{x}{3}\, =\, \left(\frac{1}{x\, +\, 2}\right)\left(\frac{3}{3}\right)\, +\, \left(\frac{x}{3}\right)\left(\frac{x\, +\, 2}{x\, +\, 2}\right)\, =\, \frac{x^2\, +\, 2x\, +\, 3}{3(x\, +\, 2)}\)

...and so forth.

Review "rational expressions" from your old algebra text, and apply the above procedures.

Eliz.