MONOTONIC

[Ryan Rigdon]

little confused with the critical points on this one. but here is my work. how does it look.

 

[BigGlenntheHeavy]

One critical point at (0,0), also point of inflection, see graph.

[attachment=0:3fvctx11]fff.jpg[/attachment:3fvctx11]

 

[Ryan Rigdon]

so are my critical points and answers to this problem look correct.

 

[BigGlenntheHeavy]

\(\displaystyle Ryan, \ I \ am \ assuming \ that \ we \ are \ looking \ for \ critical \ points \ in \ "real \ number \ land",\)

\(\displaystyle hence, \ there \ is \ only \ one, \ (0,0).\)

\(\displaystyle Descartes' \ rule \ of \ signs;\)

\(\displaystyle f(x) \ = \ 4x^5+5x^3 \ \implies \ no \ change \ in \ signs\)

\(\displaystyle f(-x) \ = \ -4x^5-5x^3 \ \implies \ no \ change \ in \ signs\)

\(\displaystyle 0 \ + \ - \ I\)
\(\displaystyle 1 \ \ 0 \ \ 0 \ \ 4 \ gives \ one \ real \ solution \ and \ four \ imaginary \ ones.\)

 

[Ryan Rigdon]

i see what you are saying. you cant have a critical point involving an i. so the only logical critical point is at (0,0) how do my other answers to the problem look.

 

[Ryan Rigdon]

are my determinations and conclusion correct for this problem.