Question

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

Answer 1

Answer:

Step-by-step explanation:

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

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

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

$f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\\frac{f(6)-f(-4)}{6-(-4)} = \frac{51-11}{10} = \frac{40}{10} = 4$