Question

Let f(x) = 3 − x . Find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

Answer 1

Answer:

The average rate of change of f(x) from x = a to x = a + h is -1

Step-by-step explanation:

Average rate of the function f(x) over [a, b] is given by:

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

Given the function:

$f(x) = 3-x$

At x=a

f(a) = 3-a

At  x = a+h

then;

f(a+h) = 3-(a+h) = 3-a-h

Using the formula for average rate of function:

$A(x) = \frac{f(x+h)-f(x)}{x+h-x}$

Substitute the given values we have;

$A(x) = \frac{3-a-h-(3-a)}{x+h-x}$

Simplify:

$A(x) = \frac{3-a-h-3+a}{h}$

or

$A(x) = \frac{-h}{h} = -1$

Therefore, the average rate of change of f(x) from x = a to x = a + h is, -1