The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by the following function.

h(w)equals=0.11w squared minus 0.2w plus 1.33

find the average rate at which a carnivorous mammal's home range increases as the animal's weight grows from 400 g to 700 g.

the average rate of change is
nothing hectares/g.

The average rate of change is defined as the slope of the secant line and is given by the formula
[f(x+h)-f(x)]/h; where h=x₂-x₁.

[f(w+h)-f(w)]/h
= [0.11(w+h)² - 0.2(w+h) + 1.33 - 0.11w² + 0.2w - 1.33] / h
= [0.11w²+0.22wh+0.11h²-0.2w-0.2h-0.11w²+0.2w] / h
= [0.22wh + 0.11h² - 0.2h] / h
= 0.22w + 0.11 h - 0.2

w₂ = 700 g and w₁ = 400 g
0.22(400) + 0.11 (700-400) - 0.2 = 120.8 hectares/g

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