Question

x−6x^(1/3)

concavity pls?

Answer 1

can you tell me where this is concave up and down pls

Answer 2

do you have the second derivative?

Answer 3

4/(3 x^(5/3))

Answer 4

looks good to me. how about the function... is it defined everywhere (continuous)?

Answer 5

think so

Answer 6

ok. so looking at your second derivative, it does not exist at x=0, correct?

Answer 7

it doesnt

Answer 8

ok. to check for concavity you'll need to split up your intervals as (-inf, 0) and (0, inf).
pick any x value in each of these intervals and stick it into the second derivative.

for each x you chose, tell me what the sign is (positive or negative)...

Answer 9

ive got a positive value on (0,inf) and negative on (-inf,0)

Answer 10

good.

Answer 11

what does a negative sign for your second derivative mean? it means the slope of the tangent line is decreasing... so the shape of your graph will look like this: