已知点A(t,t^2-1,3)B(2,-2,2)C(2,t,1),t∈R,求f(t)=AB*BC的单调递增区间
问题描述：
已知点A(t,t^2-1,3)B(2,-2,2)C(2,t,1),t∈R,求f(t)=AB*BC的单调递增区间
答
∵f(t)=AB·BC=(2-t,-2-t²+1,2-3)·(2-2,t+2,1-2)=(-2-t²+1)(t+2)+1=-t³-2t²-t-1∴f'(t)=-3t²-4t-1令f'(t)＞0得t∈(-1,-1/3)∴f(t)=AB*BC的递增区间为t∈(-1,-1/3)