1. Tardigrade
  2. Question
  3. Mathematics
  4. The function f ( x )=√ ax 3+ bx 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 x2-x-6=0. The smallest positive integral value of d is equal to

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Q. The function $f ( x )=\sqrt{ ax ^3+ bx ^2+ cx + d }$ 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

Application of Derivatives

Solution:

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, $d _{\text {smallest positive integral }}=33$.