Question

Determine when the graph is concave upward?

8/(7-x)^2

Answer 1

I thought it would be -infinity to infinity, but as it turns out it's between 2 numbers, so I'm confused.

Answer 2

what's f'(x)? what are the 0's of the numerator and denominator?

Answer 3

I got -16/(x-7)^3 for the f`(x)

Answer 4

So 7 would be the only critical number

Answer 5

okay... what's f''(x)? likewise, what are it's critical points?

Answer 6

48/(x-7)^4

So it's always positive right? (except at the vertical asymptote?)

Answer 7

yep

Answer 8

I figured since it was always positive it was always concave upward, but the online system our professor is using says that's not true

Answer 9

So I'm not sure if I took the derivatives wrong or something?

Answer 10

it's not always concave up (from neg infty to pos infty).
you have to write out the intervals:

(neg infty, 7) U (7, infty)

Answer 11

Ahh. I see. Thank you.

Answer 12

you're welcome!