Find the intervals in which the function f(x)=3/2x4-4x3-45x2+51 is a)strictly increasing b)strictly decreasing Share with your friends Share 3 Lovina Kansal answered this Dear student f(x)=32x4-4x3-45x2+51=3x4-8x3-90x2+1022f'(x)=12x3-24x2-180x2=6x3-12x2-90x=6xx2-2x-15=6xx+3x-5Here, 0,-3 and 5 are the critical pointsThe possible intervals are (-∞,-3),(-3,0),(0,5) anf (5,∞)For f(x) to be increasing, we must havef'(x)>0⇒6xx+3x-5>0⇒x∈-3,0∪5,∞So, f(x) is increasing on x∈-3,0∪5,∞For f(x) to be decreasing, we must havef'(x)<0⇒6xx+3x-5<0⇒x∈-∞,-3∪0,5So, f(x) is decreasing on x∈-∞,-3∪0,5 Regards 4 View Full Answer
