The combined resistance R of two resistors R 1 and R 2 , where R 1 , R 2 > 0 is given by 1 R = 1 R 1 + 1 R 2 . If R 1 + R 2 = C (constant), then show that the maximum resistance R is obtained by choosing R 1 = R 2 .

Here, 1 R = 1 R 1 + 1 R 2 ⇒ 1 R = R 1 + R 2 R 1 R 2 ⇒ 1 R = C R 1 C - R 1 ⇒ R = R 1 C - R 1 C ⇒ R = 1 C C R 1 - R 1 2 ⇒ d R d R 1 = 1 C C - 2 R 1 d R d R 1 = 0 ⇒ 1 C C - 2 R 1 = 0 ⇒ R 1 = C 2 d 2 R d R 1 2 = 1 C [ - 2 ] = - 2 C At R 1 = C 2 , d 2 R d R 2 = - 2 C < 0 ⇒ R has a local maxima at R 1 = C 2 But R 1 = C 2 is the only extreme point. ∴ R has maximum when R 1 = C 2 , R 2 = C - C 2 i . e when R 1 = R 2

E M B I B E

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 64

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Find the volume of the largest cylinder that can be inscribed in a sphere of radius $r cm .$

Important Questions on Application of Derivatives

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 65

Show that the semi-vertical angle of a right circular cone of maximum volume, of a given slant height, is

\tan^{- 1} \sqrt{2}

.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 66

A running track of

440

yards is to be laid out encircling a football field the shape of which is rectangle with a semi-circle at each end. If the area of the rectangular position is to be maximum find the lengths of its sides.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 67

Find the area of the largest rectangle with lower base on the