{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

finalreview1_soln

# What youll do is use lhopitals rule taking the limit

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: o. What you'll do is use l'Hopitals rule (taking the limit at x goes to 0) to find that f (x) is (well, should be) 0 at x = 0. Don't do the second derivative test unless you have a few hours to spare! Notice that f (x) is positive (same reasoning as above) for numbers really close to 0 on both the positive and negative sides of x = 0, so that f (x) is increasing through x = 0 so that we have an inflection point. 1 Or use a computer to draw the graph. This program is called Mathematica. f [x] = x 3/(Log[1 + x 2]) x3 Log[1+x2 ] Here's the graph for x between -5 and 5 (it looks like there is a critical (inflection) point near x = 0: Plot[(x 3)/(Log[1 + x 2]), {x, -5, 5}] 40 20 -4 -2 -20 2 4 -40 -Graphics- Here is the graph really close up: Plot[(x 3)/(Log[1 + x 2]), {x, -.0001, ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online