(C) Sincef0(x)<0 in(0,5)∪(5,∞), the function is decreasingin those intervals.(D) Sincef0changes from positive to negative at 0,x=0 is thex-coordinate of a local maximum by the First Derivative Test.
Thusfis concave upward on the intervals(-∞,-5)∪(5,∞)(G) The function is concave downward on the intervals(-5,5).(H) The function has no inflection points since-5 and 5 are notin the domain off.(I)Theliney=0isahorizontalasymptotesincelimx→±∞4x2-25=0.(J) Since the denominator is zero whenx=±5, we compute thefollowing limits:limx→-5-