To find concavity we need to find the second derivative. Use quotient rule to find f'(x)=4/(x+3)^2 Then use chain rule to find f''(x)=-8/(x+3)^3 To find potential inflection points, we need to find all x values where the second derivative is equal to 0 or is undefined.
Set the numerator and denominator equal to 0 and solve.
(x+3)^3=0 x+3=0 x= -3
Now plug a value less than -3 and greater than -3 into the second derivative to find where the concavity is upward (positive number).
Since f''(-4) is positive, that means that f(x) is concave up on the interval (-infinity, -3).
