Question

Is x^2-x-2 concave up or down?

Answer 1

According to my notes, if f'(x) or f''(x)>0, it should be concave up and <0 concave down. Are my notes wrong?

Answer 2

to see if something is concave up or down you should be looking for the second derivative and see whether it is negative or positive, so yeah your notes are correct.

Answer 3

It's negative. Does that mean that the original fxn is concave down in the entire domain?

Answer 4

you really need no calc for this
it is a parabola that opens up

Answer 5

I know that. It's pretty obvious but I want to understand how to do it with calc.

Answer 6

the second derivative is a constant
if the

Answer 7

\[y=ax^2+ bx+c\]
\[y'=2ax+b\\
y''=2a\]it depends entirely on the sign of the leading coefficient, just like you know

Answer 8

Oh darn. I'm stupid. calculation mistake