Mathematics: Find the average rate of change of f ( x ) = 3 x 2 − 9 on the interval [ 2 , b ] . Your answer will be an expression involving b

Find the average rate of change of f ( x ) = 3 x

Ответ:

iseestars3748

06.07.2021

Mathematics

m = 3b+6

Step-by-step explanation:

Given

f(x)=3x^2 - 9

Required

The average rate over [2,b]

Average rate (m) is calculated using:

$m = \frac{f(b) - f(a)}{b - a}$

Where

[a,b] = [2,b]

So, we have:

$m = \frac{f(b) - f(2)}{b - 2}$

Calculate f(b) and f(2)

f(x)=3x^2 - 9

f(b)=3b^2 - 9

f(2)=3*2^2 - 9 = 12 - 9 = 3

So, we have:

$m = \frac{f(b) - f(2)}{b - 2}$

$m = \frac{3b^2 - 9 - 3}{b - 2}$

$m = \frac{3b^2 - 12}{b - 2}$

Expand the numerator

$m = \frac{3b^2 + 6b-6b-12}{b - 2}$

Factorize

$m = \frac{b(3b + 6)-2(3b+6)}{b - 2}$

Factor out 3b + 6

$m = \frac{(b -2)(3b+6)}{b - 2}$

Cancel out b - 2

m = 3b+6

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Ответ:

fifthward92

28.07.2022

Mathematics

$\large\boxed{a = 22ft} \large\boxed{b = 11ft} \\\large\boxed{c = 16ft}$

Step-by-step explanation:

Side 1 = a

Side 2 = b

Side 3 = c

a = 2b

c = 5ft. + b

a + b + c = 49 feet

Substitute

2b + b + 5ft + b = 49 ft

Add the b’s

4b + 5ft = 49ft

Subtract 5ft from both sides of the equation

4b = 44ft

Divide both sides of the equation by 4 to isolate b

b = 11ft

a = b * 2 = 11 * 2 = 22ft

c = 49ft - 11ft - 22ft = 16ft

$\large\boxed{a = 22ft} \large\boxed{b = 11ft} \\\large\boxed{c = 16ft}$

Hope this helps :)

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Find the average rate of change of f ( x ) = 3 x 2 − 9 on the interval [ 2 , b ] . Your answer will be an expression involving b

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