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