A) \[\left( 15,19 \right)\]
B) \[\left( -\infty ,12 \right)\]
C) \[[12,\,15)\]
D) \[[19,\,\infty )\]
Correct Answer: D
Solution :
Given\[f(1)=-2\]and\[f'(x)\ge 4.2\]for Consider\[f'(x)=\frac{f(x+h)-f(x)}{h}\] \[\Rightarrow \]\[f(x+h)-f(x)=f'(x).h\ge (4.2)h\] So,\[f(x+h)\ge f(x)+(4.2)h\] Put x = 1 and h = 5, we get \[f(6)\ge f(1)+5(4.2)\Rightarrow f(6)\ge 19\] Hence f (6) lies in\[[19,\infty )\]
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