Question

Let f"(x)=4x^3-2x and let f(x) have critical values -1, 0, and 1. Determine which critical values give a relative maximum.

Answer 1

put those critical values into second derivative to find concave up or down. Concave down means max, concave down means min

Answer 2

So is 1 the answer?

Answer 3

what's the definition of concave up and concave down?

Answer 4

Concave up means increasing where concave down means decreasing. So to find the maximum, you plug each critical values into the function to see which value gives you the greatest number, right?

Answer 5

i meant to said f''[x]>0 means what? concave up or down? f''[x]<0 means what? up or down? f''[x]=0 means what?