Given the function f(x) = 2(3)^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Mathematics

1 answer:

sleet_krkn [62]2 years ago

8 0

Average rate of change can be calculated by determining the rate of change at x = a, and at x = b

f’(x) =2 (3^x) ln(3)

f’(0) = 2 ln(3)

f’(1) = 6 ln(3)

f’(2) = 18 ln(3)

f’(3) = 54 ln(3)

Average:

at section A = [6 ln(3) – 2 ln(3)]/1 = 4 ln(3)

at section B = [54 ln(3) – 18 ln(3)]/1 = 36 ln(3)

section B is 9 times larger.

Based from the f’(x), f’(x) varies as the power of x. so the greater of value of x, the greater the rate of change.

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When number can each term of the equation be multiplied by to eliminate the fractions before solving 6-3/4x+1/3=1/2x+5

PolarNik [594]

Answer:

Step-by-step explanation:

You need to find the least common denominator (LCD) to all the denominators of the fractions present in the equation. These denominators are (writing them in their prime factor form to make our calculations easier):

$4=2^2\\3=3\\2=2$

Therefore, we need to include a factor of 3, and two factors of 2 ( $2^2$ ) in our least common denominator, so this LCD will be a perfectly divided by all three given denominators, therefore eliminating all fractions in the equation.