Task list filter?

Choose required ranks and required tasks. The table of contents will list only tasks having one of the required ranks in corresponding rankings and at least one of the required tags (overall). If you wish to filter only according to some rankings or tags, leave the other groups empty.

Task rankings

Difficulty level

Task tags

Task type
«
«
«

An increasing implicit function

Task number: 3223

For the relation x2+2xy2+y4−y5=0. Prove following.

  • Variant 1

    This relation defines a smooth function y=f(x) in some neighborhood of the point 0, for which f(0)=1 holds.

  • Variant 2

    The function f is increasing in some neighborhood of the point 0.

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
Send comment on task by email