Question

Which correctly describes the concavity of the function
f(x) = x^3 – 5x + 7?

Answer 1

which which?

Answer 2

3x^2 - 5 = 0
x^2 = 5/3
x = + or - 5/3

Answer 3

now:
6x, is f '' so when is that positive?

Answer 4

-infinity to -1.666, -1.666 to +1.666 or 1.666 to infinity?

Answer 5

is the concave downward or upward though?

Answer 6

a cubic has 2 concavities; one is cave down the other is cave up; just depends on where you are at on it

Answer 7

your question inplies that there are options to choose from

Answer 8

so:
try -2:
6*(-2) = -12, therefore conc down on (-inf; 1.66)

Answer 9

i meant (-inf; -1.6)

Answer 10

6*1 = 6, therefore concave up on (-1.6,1.6)

Answer 11

what about (-3.0)? that would be 6 so concave upward? Am I on the right track?

Answer 12

No where did u get (-3,0) from?

Answer 13

one of the question answers. lol. along with downward interval at 0,3 upward at 0,3 or downward at-3,3.Those are just some question choices. I wanted to learn how to do it so i could figure out how to plug in the answers myself. lmao

Answer 14

okay look just take a number from any of those intervals, like say x=-2 which is inside -3,0
and plug that into 6x. If it's negative then it's concave down, positive - conc up

Answer 15

so from the point -3,3 the answer is -18,18 so the concave is downward?

Answer 16

sorry, i still cant make out what it is your asking for :/

Answer 17

arggg. This is the question: Which correctly describes the concavity of the function
f(x) = x^3 – 5x + 7?

concave upward in the interval (-3, 0)
concave downward in the interval (0, 3)
concave upward in the interval (0, 3)
concave downward in the interval (-3, 3)

Answer 18

Those are the different options. I didnt know those answers were necessary. I wanted to try to figure it out on my own. Lol