Question

Which of the following statements is/are correct?
1. f(x) is increasing in the interval [-1, 2].
2. f(x) is decreasing in the interval (2, 3].
Select the correct answer using the code given below

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is C Both 1 and 2

$f\left(x\right)=3x^2+12x-1,-1\le x\le 2$

$f^{{}^{\prime }}\left(x\right)=6x+12$

So, for $-1\le x\le 2,$ $f^{{}^{\prime }}\left(x\right)>0$

So, f(x) is increasing in $[-1,2]$

$f\left(x\right)=37-x,2<x\le 3$

$f^{{}^{\prime }}\left(x\right)=-1$

So, for $-2<x\le 3$ $f^{{}^{\prime }}\left(x\right)<0$

So, f(x) is decreasing in $(2,3]$

So, the answer is option (C)