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

Step-by-step explanation:

Given

Required

The average rate over

Average rate (m) is calculated using:

Where

So, we have:

Calculate f(b) and f(2)

So, we have:

Expand the numerator

Factorize

Factor out 3b + 6

Cancel out b - 2

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~