Mathematics

Problem

For the differentiable, strictly decreasing function

y = f(x)

, it is known that

f(4) = 5

and

f'(4) = -4

. A quantity

K

(joules) depends on

x

K(x) = x^{3} + 1

. At the instant when

y = 5

, the variable

y

is increasing at a rate of

0.8

units per second. Compute the instantaneous rate

\frac{dK}{dt}

in joules per second at that moment.