Question

The function $f(x)=\sqrt{a{x}^3+b{x}^2+cx+d}$ has its non-zero local minimum and local maximum values at -2 and 2 respectively. Given ' $a$ ' is root of the equation $x^2-x-6=0$.
The smallest positive integral value of $d$ is equal to

• A. 1
• B. 32
• C. 33
• D. 34

Answer 1

Answer: (C)

Since, minimum and maximum values are non-zero, so both $g(-2)>0$ and $g(2)>0$.
Now, $g(-2)>0\Rightarrow d>32$
Also, $g(2)>0\Rightarrow d>-32$
Then, $a=-2,b=0,c=24,d>32$
Hence, $d_{\text{smallest positive integral }}=33$.