Use interval notation to indicate where f(x) in increasing

Question

f(x)= 4x - 2 / x+7

Use interval notation to indicate where f(x) is increasing and where it is decreasing

 

ALSO

 

use interval notation to indicate where f(x) is concave up or down

Answer 1

Assuming that the function is f(x) = (4x-2)/(x+7),

 

f'(x) = [4(x+7)-(4x-2)]/(x+7)² = 30/(x+7)²>0 for all x ≠ -7

 

So, f is increasing on (-∞,-7)∪(-7,∞).  There are no intervals on which f is decreasing since f'(x) is never negative.    

 

f"(x) = -60(x+7)^-3 = -60/(x+7)³

 

f"(x) > 0 when x < -7 and f"(x) < 0 when x > -7

 

f is concave up on (-∞,-7) and is concave down on (-7,∞).