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allochka39001 [22]
2 years ago
15

What is the average rate of change of the function over the interval x = 0 to x = 6? f(x) = (2x - 1) / (3x + 5)

Mathematics
1 answer:
Sedaia [141]2 years ago
5 0

Answer:

The average rate of change of the function over the interval x = 0 to x = 6 is \frac{34}{195}.

Step-by-step explanation:

Geometrically speaking, the average rate of change (r) of the function over a given interval is determined by equation of secant line, that is:

r = \frac{f(b)-f(a)}{b-a} (1)

Where:

a, b - Lower and upper bounds.

f(a), f(b) - Function evaluated at lower and upper bounds.

If we know that f(x) = \frac{2\cdot x -1 }{3\cdot x + 5}, a = 0 and b = 6, then the average rate of change of the function over the interval is:

f(a) = \frac{2\cdot (0)-1}{3\cdot (0) +5}

f(a) = -\frac{1}{5}

f(b) = \frac{2\cdot (6)-1}{3\cdot (6)+5}

f(b) = \frac{11}{13}

r = \frac{\frac{11}{13}-\left(-\frac{1}{5} \right) }{6-0}

r = \frac{34}{195}

The average rate of change of the function over the interval x = 0 to x = 6 is \frac{34}{195}.

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