Question

1. find the average rate of change of ( f(x)=x^{2}+3x - 7 ) from ( x=-1 ) to ( x = 4 ).

Explanation:

Step1: Calculate f(-1)

$f(-1) = (-1)^2 + 3(-1) -7 = 1 -3 -7 = -9$

Step2: Calculate f(4)

$f(4) = (4)^2 +3(4) -7 =16 +12 -7=21$

Step3: Compute average rate of change

$\text{Average rate} = \frac{f(4)-f(-1)}{4 - (-1)} = \frac{21 - (-9)}{5} = \frac{30}{5}=6$

Answer:

6