NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 5

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Question 14:

Find the area of greatest rectangle that can be inscribed in an ellipse


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)

Question 16-Point on the ellipse

Point on the Ellipse

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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



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


Let ABC be an isosceles triangle inscribed in the circle with radius a such that .

(see fig. 16.4)

ABC be an isosceles triangle inscribed in the circle with ra …

ABC be an Isosceles Triangle Inscribed in the Circle Radius

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Therefore, area of the triangle ABC i.e.



Therefore, Area of triangle is maximum when