For the function f(x, y) = y^2 + 3x^6 + 5y^4 identify whether the following points are local min's, local max's, or inflection points a) (0,0) c) is the function convex? why or why not?

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.

1/8 3/16 3/4

step-by-step explanation:

you put them as all the same denominator and multiply

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)