Question

The mass of a cube in grams is M=x^3+0.1x^4, where x is the length of one side in centimeters. If the length is increasing at a rate of 0.03 cm/hr, at what rate is the mass of the cube increasing when its length is 6 cm?

Answer 1

Answer:

5.832 g/h

Explanation:

We can find the rate of mass relative to time by taking the derivative of M

$M' = \frac{dM}{dt} = \frac{dM}{dx}\frac{dx}{dt}$

$M' = \frac{d(x^3 + 0.1x^4)}{dx}\frac{dx}{dt}$

$M' = (3x^2 + 0.4x^3)x'$

We can plug in the current length x = 6 cm and current length rate 0.03 cm/h

$M' = (3*6^2 + 0.4*6^3)0.03 = 5.832 g/h$