Asked by Henry

THANK YOU TUTORS SO MUCH FOR YOUR HELP

Determine the intervals on which the function is concave up or concave down.

I finally understand that when f'' is greater than 0 it means concave up.

f(X) = 18x^2 + x^4

so I differentiate that to be
36x + 4x^3 that is f'
if I differentiate again I get:
f'' = 36+12x^2

it's from here that I get lost. At what intervals does it represent concave up or down? and what is my next step after getting f''?
Answered by Steve
look at f" - it is always positive
so, f is always concave up

just looking at it you can see that f(0) = 0, and always goes up on each side.
Answered by Henry
Right, but I am unsure what to put for intervals of concave up :/
Answered by Steve
how about (-oo,+oo) ?
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