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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $a>0$. If the function $f(x)=6x^3-45ax^2+108a^2x+1$ attains its local maximum and minimum values at the points $x_1$ and $x_2$ respectively such that $x_1x_2=54$, then $a+x_1+x_2$ is equal to
Solution
$f(x)=6x^3-45ax^2+108a^2x+1$$f'(x)=18x^2-90ax+108a^2$
$=18(x^2-5ax+6a^2)$
So critical points:
$x_1,x_2=2a,3a$
Given $x_1x_2=54$
⇒ $6a^2=54 \Rightarrow a^2=9$
$ \Rightarrow a=3$ (since $a>0$)
$x_1+x_2=5a=15$
$a+x_1+x_2=3+15=18$
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