Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-10

For any real number x, the maximum value of \[4-6x-{{x}^{2}}\]

A) 4

B) 7

C) 9

D) 13

Correct Answer: D

Solution :

Let the given equation be represented as

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

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

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

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

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

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

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

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

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

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

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

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

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

So, the maximum value of \[=4-6x-{{x}^{2}}\]is 13.