If f(x) is twice differentiable function in [c1−1,c2+1] and f′(c1)=f′(c2)=0,f′′(c1)⋅f′′(c2)<0,f(c1)=9,f(c2)=0. Let k and m be the minimum number of the roots of f(x)=0 and f′(x)=0 respectively,in [c1−1,c2+1] List - IList - II(I) If f′′(c1)−f′′(c2)>0,then k = (P) 1(II) If f′′(c1)−f′′(c2)<0,then k = (Q) 2(III) If f′′(c1)−f′′(c2)>0,then m = (R) 3(IV) If f′′(c1)−f′′(c2)<0,then m = (S) 4 Which of the following is only CORRECT combination?

If f(x) is twice differentiable function in [c1−1,c2+1] and f′(c1)

1.	If f(x) is twice differentiable function in [c1−1,c2+1] and f′(c1)=f′(c2)=0,f′′(c1)⋅f′′(c2)<0,f(c1)=9,f(c2)=0. Let k and m be the minimum number of the roots of f(x)=0 and f′(x)=0 respectively,in [c1−1,c2+1] List - IList - II(I) If f′′(c1)−f′′(c2)>0,then k = (P) 1(II) If f′′(c1)−f′′(c2)<0,then k = (Q) 2(III) If f′′(c1)−f′′(c2)>0,then m = (R) 3(IV) If f′′(c1)−f′′(c2)<0,then m = (S) 4 Which of the following is only CORRECT combination?
Answer» If $f (x)$ is twice differentiable function in $[c_{1} - 1, c_{2} + 1]$ and $f^{'} (c_{1}) = f^{'} (c_{2}) = 0, f^{''} (c_{1}) \cdot f^{''} (c_{2}) < 0, f (c_{1}) = 9, f (c_{2}) = 0$ . Let $k$ and $m$ be the minimum number of the roots of $f (x) = 0$ and $f^{'} (x) = 0$ respectively,in $[c_{1} - 1, c_{2} + 1]$ $\begin{matrix} List - I & List - II (I) If f^{''} (c_{1}) - f^{''} (c_{2}) > 0, then k = & (P) 1 (II) If f^{''} (c_{1}) - f^{''} (c_{2}) < 0, then k = & (Q) 2 (III) If f^{''} (c_{1}) - f^{''} (c_{2}) > 0, then m = & (R) 3 (IV) If f^{''} (c_{1}) - f^{''} (c_{2}) < 0, then m = & (S) 4 \end{matrix}$ Which of the following is only CORRECT combination?