Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-44

For any real number x, the maximum value of \[4-6x-{{x}^{2}}\]is                                    [SSC (CGL) 2014]

A) 4

B) 7

C) 9

D) 13

Correct Answer: D

Solution :

Let the given equation be represented as

\[\text{f}\,(x)=4-\,\,6x-{{x}^{2}}\]

Now, differentiating above function w.r.t. x, we get

\[\text{f}'\,\,(x)=-\,\,6-2x\]

For value of x put \[\text{f}'(x)=0\]

\[-\,\,6-2x=0\]

\[\therefore \] \[x=-\,\,3\]

For maximum value, we take \[\text{f}'(x)\]

\[\text{f}'(x)=-\,2\]

Since, value of \[\text{f}'(x)\] is negative.

So, \[\text{f}\,(x)\] is maximum at \[x=\,\,-3.\]

Putting \[x=-\,\,3\]in \[\text{f}\,(x),\] we get

\[\text{f}\,(-\,\,3)=4\,\,-(6)(-\,\,3)-{{(-\,\,3)}^{2}}\]

\[=4+18-9=13\]

The maximum value of \[4-6x-{{x}^{2}}\] is 13.