NEET (2024 Updated)-National Eligibility cum Entrance Test (Medical) Chemistry Coaching Programs
πΉ Video Course 2024 (8 Lectures [4 Hrs : 33 Mins]): Offline Support
Click Here to View & Get Complete Material
Rs. 100.00
1 Month Validity (Multiple Devices)
β³ π― Online Tests (5 Tests [50 Questions Each]): NTA Pattern, Analytics & Explanations
Click Here to View & Get Complete Material
Rs. 500.00
3 Year Validity (Multiple Devices)
π Study Material (159 Notes): 2024-2025 Syllabus
Click Here to View & Get Complete Material
Rs. 350.00
3 Year Validity (Multiple Devices)
π― 3111 MCQs (& PYQs) with Full Explanations (2024-2025 Exam)
Click Here to View & Get Complete Material
Rs. 650.00
3 Year Validity (Multiple Devices)
NCERT Class 12- Mathematics: Chapter β 6 Application of Derivatives Part 5
Question 14:
Find the area of greatest rectangle that can be inscribed in an ellipse
Answer:
Let be the rectangle of maximum area with sides and , where is a point on the ellipse as shown in the Fig. 6.3. The area A of the rectangle is i.e.. , which gives (say)
Therefore,
Again,
Now,
At
Thus at is maximum and hence the area A is maximum.
Maximum area units.
Question 17:
Find the difference between the greatest and least values of the function , on
Answer:
Therefore,
Clearly, is the greatest value and is the least.
Therefore, difference
Question 18:
An isosceles triangle of vertical angle is inscribed in a circle of radius . Show that the area of triangle is maximum when
Answer:
Let ABC be an isosceles triangle inscribed in the circle with radius a such that .
(see fig. 16.4)
Therefore, area of the triangle ABC i.e..
Therefore,
Therefore,
Therefore, Area of triangle is maximum when