Let denote the temperature

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

Problem

Let

T(r)=5r^{3}-2r

denote the temperature, in degrees Celsius, on the surface of an expanding metal sphere whose radius

r

is measured in centimeters. When

r=2\text{ cm}

the radius is increasing at a rate of

0.1\text{ cm/min}

. What is

\dfrac{dT}{dt}

, in degrees Celsius per minute, at that instant? (a)

58

(b)

5.8

(c)

4.1

(d)

-5.8