Question

for the function ( y = x^{2} ), compute the average rate of change between ( x = 7 ) and ( x = 10 ).
the average rate of change is
(simplify your answer.)

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( y = f(x) \) between \( x = a \) and \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \).

Step2: Find \( f(7) \) and \( f(10) \) for \( f(x)=x^{2} \)

For \( x = 7 \), \( f(7)=7^{2}=49 \).
For \( x = 10 \), \( f(10)=10^{2}=100 \).

Step3: Substitute into the average rate of change formula

Here, \( a = 7 \), \( b = 10 \), \( f(a)=49 \), \( f(b)=100 \).
So, the average rate of change is \( \frac{f(10)-f(7)}{10 - 7}=\frac{100 - 49}{3}=\frac{51}{3}=17 \).

Answer:

17