Solutions to Tricky Problems

# Solutions to Tricky Problems - Solutions to Tricky problems...

This preview shows pages 1–2. Sign up to view the full content.

1. The answer is (e). The curves meet in three places, ( - 2 , 4) , (0 , 0) and (3 , 9). The region between the curves is made up of a pair of leaf-shaped regions touching at the point (0 , 0). The x -intervals for the two regions are [ - 2 , 0] and [0 , 3]. In the ﬁrst region, y goes from x 2 to x 3 - 6 x , while in the second region it is the other way around. Therefore, (c) would be right except that I forgot to change the x -limits on the second region; the correct answer is therefore (e). 2. The answer is (b). In (a) there is nothing distinguishing a maximum from a minimum. In (c) it is possible that the minimum is elsewhere on the boundary, for example at the origin. In (d) there is not a minimum in the interior, but it could be on one of the other boundary segments. To see that it is (b) and not (e), notice that if f x and f y are both greater than zero, then there can be no maximum on the interior (because the gradient does not vanish), on the interior of the x -axis segment (because f x > 0), on the interior of the y -axis (because f y > 0), or at the origin (because D u > 0 for any u pointing into the triangle). Any continuous function on a closed bounded set has a maximum (see page

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### Page1 / 3

Solutions to Tricky Problems - Solutions to Tricky problems...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online