Question

Find the average rate of change of f ( x ) = 7x^2 − 6 on the interval [ 3 , a ] . Your answer will be an expression involving a

Answer 1

Answer:

$\frac{7a^2-63}{a-3}$

Step-by-step explanation:

So what is the average rate of change?  Basically, it's the slope.  In fact it's exactly the slope for a linear equation, but how do you find slope?

$\frac{y_2-y_1}{x_2-x_1}$

Sp we just plug the values in.  

$x_1=3\\x_2=a\\y_1=7(3)^2-6=63-6=57\\y_2=7(a)^2-6$

$\frac{7a^2-6-57}{a-3}=\frac{7a^2-63}{a-3}$