The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by $H(w)=0.11{w}^{1.36}$

a)Find the average rate at which a carnivorous mammal's home range increases as the animal's weight grows from 200g to 450g.

b) Find $\frac{H(500)-H(400)}{500-400}$, and interpret this result.

a)Find the average rate at which a carnivorous mammal's home range increases as the animal's weight grows from 200g to 450g.

b) Find $\frac{H(500)-H(400)}{500-400}$, and interpret this result.