Question

calculate the average rate of change from (x = - 2) to (x = 1) of the function. (f(x)=x^{2}+5x - 12) first, find the change in (y) by evaluating the function at (-2) and (1): (f(-2)=) (f(1)=) the change in (y) is now find the change in (x). the change in (x) is the average rate of change of (f(x)=x^{2}+5x - 12) from (x=-2) to (x = 1) is

Explanation:

Step1: Evaluate f(-2)

Substitute $x = - 2$ into $f(x)=x^{2}+5x - 12$:
$f(-2)=(-2)^{2}+5\times(-2)-12=4 - 10 - 12=-18$

Step2: Evaluate f(1)

Substitute $x = 1$ into $f(x)=x^{2}+5x - 12$:
$f(1)=1^{2}+5\times1-12=1 + 5 - 12=-6$

Step3: Calculate change in y

$\Delta y=f(1)-f(-2)=-6-(-18)=-6 + 18 = 12$

Step4: Calculate change in x

$\Delta x=1-(-2)=1 + 2=3$

Step5: Calculate average rate of change

The average rate of change is $\frac{\Delta y}{\Delta x}=\frac{12}{3}=4$

Answer:

4