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

http://www.wolframalpha.com/input/?i=f%28x%29%3D+sqrt%28x%5E2+%2B+9%29+-+x

Answer 2

Use the first derivative to see where it is increasing or decreasing. If it is positive, f is increasing; if it is negative, f is decreasing.
Use the second derivative to see where it is concave up and down. If it is positive, f is concave up; the opposite if not. The infinite limit tells you f has a horiz asymptote of y = 0.

Answer 3

so take the first derivative, graph it and see where its increasing?

Answer 4

- Take derivative.
- Set derivative = 0. Solve for x.
- See the sign of the derivative between the intervals of where x = 0 and +/- inf.
- If the sign of the derivative is positive on the interval, then f is increasing on the interval. The opposite for negative.

Answer 5

i cant get a solution for the derivative equal to zero

Answer 6

Then the derivative is always positive or negative?