Question

prove that the real function x -> 3x^4 + 4x^3 + 6x^2 + 1 is positive

Answer 1

you know some calculus?

Answer 2

i just know that the first step is to differentiate. but i don't understand how to prove it's positive :(

Answer 3

find the minimum value using calculus...show that your function is positive at its min value

Answer 4

you can also show it is positive (in part) by factoring

Answer 5

\[3x^4 + 4x^3 + 6x^2 + 1=x^2(3x^2+4x+6)+1\]

show that \(3x^2+4x+6\) is always positve