Discussion
The maximum value of the function \(f(x) = x\sqrt{4x - x^{2}}\) is
Answer: D
The maximum value is \(3\sqrt{3}\).
The domain is \(0 \le x \le 4\). Maximise \(f^{2} = x^{2}(4x - x^{2}) = 4x^{3} - x^{4}\):
\[ \begin{aligned} \frac{d}{dx}(4x^{3} - x^{4}) &= 12x^{2} - 4x^{3} = 4x^{2}(3 - x) \\ x = 3: \ f &= 3\sqrt{12 - 9} = 3\sqrt{3} \end{aligned} \]
The function is 0 at both ends of the domain, so this critical point gives the maximum. \(4\sqrt{3}\) and \(6\sqrt{3}\) evaluate the root at the wrong point, and \(\sqrt{3}\) forgets the factor x.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development