Determine the intervals on which the function is concave up and concave down

f(x) = 17x^2 = x^4

by differentiating I get
f'(x) = 34x+4x^3

and then I get lost. Can someone finish this up?

1 answer

f'' > 0 => concave up.

f''(x) = 34+12x^2
since f'' is always positive, f is always concave up.

you can see that because x^2 and x^4 are always positive, and always increasing when x is nonzero.

also, f' = 2x(2x^2+17) which is zero only at x=0. So, only one turning point at (0,0)