Question

If f(x) = x2 + 2x + 3, what is the average rate of change of Rx) over the interval (-4, 6]?

Answer 1

Explanation:

The average rate of change of a function over an interval is simply the slope over the interval because:

`let \: g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a}(the\:average\:value\:of\:g)=(f(b)-f(a))/(b-a)`

We have to know f(6) and f(-4)

`f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\(f(6)-f(-4))/(6-(-4)) = (51-11)/(10) = (40)/(10) = 4`