Question

consider the function f(x)= sqrt(x^2 + 9) - x

f(x) is increasing on the interval ?
f(x) is decreasing on the interval?
f(x) is concave up on the interval ?
f(x) is concave down on the interval ?
f(x) has a horizontal asymptote y=?

Answer 1

find f' first

Answer 2

i tried

Answer 3

http://www.wolframalpha.com/input/?i=graph+sqrt%28x%5E2+%2B+9%29+-+x
the function is decreasing everywhere

it's usual process that you did before.

Answer 4

(x)/(sqrt(x^2 + 9)) - 1

Answer 5

what about concave

Answer 6

okay find the critical points by equating to zero .. what do you get.

Answer 7

wait thats the first derivative, i was able to get the inc and dec, now i just need the concaves

Answer 8

the values of first derivative are nowhere positive

Answer 9

yea i figured that

Answer 10

to find the concaves, i take the second derivative right

Answer 11

yes ,,, find second derivative.
put the values, and if it's positive then it's concave upwards
if it's negative, then it's concave downwards.

Answer 12

phew i got it.

Answer 13

thanks

Answer 14

can you just solve this one for me please, i have tried the longest

(x−5)^9(x−2)^4(x+10)^8

find where its increasing