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Andreas93 [3]
2 years ago
15

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

Mathematics
1 answer:
JulijaS [17]2 years ago
3 0

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

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