Question

Let f(x)=x2−2x−4 . What is the average rate of change for the quadratic function from x=−1 to x = 4?

Answer 1

The average rate of change x=−1 to x = 4 is 

A= f(4) -f(-1) / 4- (-1)
f(4)=4²-2x4-4=16-12=4
f(-1)=1+2-4= -1
f(4) -f(-1) / 4- (-1) = 4-(-1)/4-(-1)= 5/5=1
the rate of change is A=1

Answer 2

Answer:

The average rate of change for f(x) from x=−1 to x = 4 is, 1

Step-by-step explanation:

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

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

As per the statement:

$f(x) = x^2-2x-4$

we have to find the average rate of change from x = -1 to x = 4

At x = -1

$f(-1) = (-1)^2-2(-1)-4 = 1+2-4 = -1$

and

at x = 4

$f(4) = (4)^2-2(4)-4 = 16-8-4 = 4$

Substitute these in [1] we have;

$A(x) = \frac{f(4)-f(-1)}{4-(-1)}$

⇒$A(x) = \frac{4-(-1)}{4+1}$

⇒$A(x) = \frac{5}{5}$

Simplify:

A(x) = 1

Therefore, the average rate of change for f(x) from x=−1 to x = 4 is, 1