Question

A given temperature the heat loss of an organism is y = 33x 3

where y is the heat loss in watts and x is the length of the
organism in metres. What is the rate of change of heat loss when
the organism is 0.8 m in length?

Answer 1

63.36 W/m

Explanation:

The heat loss of an organism is given by :

`y=33x^3` ...(1)

Where

y is heat loss in watts and x is the length of the organism in metres.

We need to find the rate of change of heat loss when the organism is 0.8 m in length.

Differentiate equation (1) wrt x.

`(dy)/(dx)=(d)/(dx)(33x^3)\\\\=33* 3x^2\\\\=99x^2`

Put x = 0.8 m in above equation.

`(dy)/(dx)=99* (0.8)^2\\\\=63.36\ W/m`

So, the rate of change of heat loss when the organism is 0.8 m in length is 63.36 W/m