Question

I have a question:
So, Determine if y = -2x3 + 3x2 + 36x - 7 is concave up, concave down, or neither concave
up nor concave down on the interval (0; 2). Justify your answer. So I tried figuring this out and the answer I got was wrong. The correct answer somehow is "neither." My question is, WHY?! It makes no sense when I am doing it.

Thank you!

Answer 1

Dammit! I'm sorry, that is supposed to be x^3 and x^2 for the function. I apologize for my repetitive mistakes.

Answer 2

it is this
\[f(x)=-2x^3 + 3x^2 + 36x - 7 \]?

Answer 3

yes it is!

Answer 4

take the derivative twice
what do you get?

Answer 5

Hold on. Let me do this right.

Answer 6

Okay I got -12x+6

Answer 7

ok

Answer 8

yes that is it

Answer 9

so if the second derivative is positive, function is concave up

Answer 10

\[-12x+6>0\iff x<\frac{1}{2}\]

Answer 11

Right, I got that.

Answer 12

since it changes concavity at \(\frac{1}{2}\) it is not concave up on the entire interval \((0,2)\) not is it concave down on that entire interval. it changes concavity in that interval

Answer 13

*nor

Answer 14

Oh! Okay I think I got it. So just on that interval because it is from (0,2), it isn't concave up for the entire thing, correct? It basically gets cut off?

Answer 15

Wouldn't it make it an inflection point though?

Answer 16

yes it is a weird question i think

Answer 17

Because if it changes, I would think that...?

Answer 18

seems like they should just ask "where is it concave up and concave down?" but whatever

Answer 19

I see. I think I understand it now. Thank you! This has been bothering me all day!

Answer 20

yw