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Sveta_85 [38]
2 years ago
13

F(x)=x 3−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x What is the average rate of change of f over

the interval [2,6] open bracket, 12, comma, 6, close bracket?
Mathematics
1 answer:
mel-nik [20]2 years ago
4 0

Answer:

A(x) = 243

Step-by-step explanation:

Given

f(x) = x^3 - 9x

Interval: (12,6)

Required

Determine the average rate of change

Average rate is calculated as thus;

A(x) = \frac{f(b) - f(a)}{b - a}

<em>In this case; b = 12 and a = 6</em>

Calculating f(12)

f(12) = 12^3 - 9 * 12

f(12) = 1728 - 108

f(12) = 1620

Calculating f(6)

f(6) = 6^3 - 9 * 6

f(6) = 216 - 54

f(6) = 162

Substitute 12 for b and 6 for a in A(x) = \frac{f(b) - f(a)}{b - a}

A(x) = \frac{f(12) - f(6)}{12 - 6}

Substitute values for f(6) and f(12)

A(x) = \frac{1620 - 162}{12 - 6}

A(x) = \frac{1458}{ 6}

A(x) = 243

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