The power output (in watts) of a certain machine after hours of operation is

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The power output (in watts) of a certain machine after

t

hours of operation is

P(t)=200t-t^{2}

, while the energy consumption rate (in watts) is

C(t)=100+2t

. The operational efficiency is defined as

E(t)=\dfrac{P(t)}{C(t)}

. For what value of

t

(in hours) is the efficiency maximized during the interval

0<t<100

? (a)

41

(b)

62\text{ (approximately)}

(c)

50

(d)

82