concave up or concave down.

Question

Consider the function f(x)=2x+8/5x+2. For this function there are two important intervals: (−∞,A) and (A,∞) where the function is not defined at .

Find  

  For each of the following intervals, tell whether f(x) is increasing or decreasing.

(−∞,A)=

 (A,∞)=

 Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) is concave up or concave down.(−∞,A)=

 (A,∞)=

Answer 1

f(x) = (2x + 8)/(5x + 2) = 2/5 + 36/(25x + 10)

5x + 2 = 0 at x = -2/5

Thus, A = -2/5

f(x) is decreasing on (-∞, -2/5) and (-2/5, ∞)

f(x) is concave down on (-∞, -2/5) and concave up (convex) on (-2/5, ∞)