Question

x^2/2 + 4/x when is it concave up?

Answer 1

you first! hehehe

Answer 2

ha so i tried finding second derivative but got different answers than the answer choices so i figured i would start over

Answer 3

ok, show me steps

Answer 4

should i do quotient rule?

Answer 5

sooo do i use quotient rule on each term

Answer 6

ohhhh you can pull out the coefficient

Answer 7

so f'=

Answer 8

\[(\dfrac{x^2}{2}+\dfrac{4}{x})' = x -\dfrac{4}{x^2}\]

Answer 9

correct. i typed it wrong

Answer 10

\[(x -\dfrac{4}{x^2})' = 1+ \dfrac{8}{x^3}\]

Answer 11

now, make it the same denominator, you have
f"(x) = \(\dfrac{x^3+8}{x^3}\)

Answer 12

ok
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Answer 13

for the numerator, you have x = -2 , and 2 complex roots, but ignore the complex roots, so, so far you have x =-2 make f"(x) = 0 ok?

Answer 14

ya

Answer 15

and with x >-2 the numerator >0 ok?

Answer 16

just numerator, not the whole thing yet, Please, be patient

Answer 17

so then the denom has a critical number of 0

Answer 18

stop

Answer 19

yes sir

Answer 20

you should understand what I am saying first

Answer 21

i do understand that

Answer 22

with x <-2 the numerator <0 OK?