Math  /  Calculus

QuestionThe function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval 8x6?-8 \leq x \leq-6 ?

Studdy Solution

STEP 1

1. The function f(x) f(x) is continuous on the interval [8,6][-8, -6].
2. The points (8,16)(-8, 16) and (6,12)(-6, 12) are on the graph of f(x) f(x) .

STEP 2

1. Understand the concept of average rate of change.
2. Identify the relevant points on the graph.
3. Calculate the average rate of change using the formula.

STEP 3

The average rate of change of a function over an interval [a,b][a, b] is given by the formula:
Average Rate of Change=f(b)f(a)ba\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}

STEP 4

Identify the points on the graph that correspond to x=8 x = -8 and x=6 x = -6 .
From the graph, the points are (8,16)(-8, 16) and (6,12)(-6, 12).

STEP 5

Substitute the values from the identified points into the average rate of change formula:
Average Rate of Change=f(6)f(8)6(8)\text{Average Rate of Change} = \frac{f(-6) - f(-8)}{-6 - (-8)}
=12166+8= \frac{12 - 16}{-6 + 8}
=42= \frac{-4}{2}
=2= -2
The average rate of change of the function f(x) f(x) on the interval [8,6][-8, -6] is:
2 \boxed{-2}

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