I having trouble getting the x value for the second derivative. could someone help me?

[native aurora]

whats your second derivative

[bright prawn]

I got -2/9(x-5)^4/3

[leaden radish]

It is -2/9(x-5)^-4/3

[bright prawn]

Would the x values be 5?

I’m trying to get the concavity

@leaden radish

[native aurora]

that would be your inflection point

check for the signs of your second derivative function

[leaden radish]

use the intervals x<5 and x>5

[bright prawn]

so i would be looking for the signs of (-infinity 5)(5 infinity

[native aurora]

yes

[leaden radish]

if f''(x)> 0 , the point is concave upwards and if f''(x)<0 the point is concave downwards

[bright prawn]

@leaden radish so would the concavity of this particular question be facing upwards on (-infinity, 0)

[native aurora]

-infinity, 5

not 0

5 is your inflection point, meaning its the point where your function changes its concavity

[bright prawn]

so i plugged it in and that particalar point would be facing upwards correct

and the other side 5, infintity would be facing downwards

[native aurora]

yes

wait no, your function would actually be concave upwards from (5, infinity) since f"(x)<0 in that interval

[bright prawn]

would the previous thing that i said about the other side right

[native aurora]

no, it would be the other way around

[leaden radish]

Actually, did you try to plug it on a graph calculator?

[native aurora]

concave downwards from -infinity, 5

you dont need a graph calculator, just check for the signs of the function

[leaden radish]

Yeah, but I think its concave downwards throught all the interval

[bright prawn]

ok thanks, also for part c. i got 7 as the abosolute max and would 5 be the absolute min or would there be non

at 0 it would be underfined

[native aurora]

thats not true...

[native aurora]

hold on

[native aurora]

yes 5 would be the absolute min because it's the local minimum of the function and it belongs to that interval

ok nvm

yea it is

a local min

[bright prawn]

so 7 is absolute max then

[native aurora]

mhm

[bright prawn]

thanks for the help

[leaden radish]

check this

[native aurora]

that is a concave upwards from (-infinity to 5)....

the function is just a little thin

[leaden radish]

but then the result for f''(4) should be positive

Wait, actually there are no inflection points, x=5 is a vertical asymptote

[native aurora]

you're right

theres no inflection point

@bright prawn

[leaden radish]

@native aurora could you check my post please? Just to check if I didn't miss something.. thanks

[native aurora]

no you didn't miss anything, it can't be an inflection point as you said

i did a miscalculation on my end, mb

[leaden radish]

oh, I mean another post that I made on the help-forum, not this one haha

[native aurora]

tag me in it