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Sveta_85 [38]
3 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]3 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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phil ate three less than twice as many pancakes as sara. together they combined to eat 15 pancakes. How many pancakes did each e
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Answer:

Let x represents the Sara eat pancake and y represents the Phil eat the pancake.

As per the statement:

Phil ate three less than twice as many pancakes as Sara.

"Twice as many pancake as Sara" means 2x

"three less than twice as many pancakes as Sara" means 2x -3

⇒y = 2x-3         .....[1]

It is also given that together they combined to eat 15 pancakes.

⇒x+y =15      .....[2]

Substitute equation [1] into [2] we get;

x+2x-3 = 15

Combine like terms;

3x-3 =15

Add 3 to both sides we get;

3x = 18

Divide both sides by 3 we get;

x = 6

Substitute the value of x in [1] we get;

y = 2(6)-3 = 12-3 =9

y = 9

Therefore, the pancakes did each eat are;

Sara eat pancake = 6 and Phil eat pancake = 9


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