Respuesta :

loumast

Answer:

[tex]\frac{7a^2-63}{a-3}[/tex]

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?

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Sp we just plug the values in.  

[tex]x_1=3\\x_2=a\\y_1=7(3)^2-6=63-6=57\\y_2=7(a)^2-6[/tex]

[tex]\frac{7a^2-6-57}{a-3}=\frac{7a^2-63}{a-3}[/tex]

akposevictor

The average rate of change of [tex]f ( x ) = 7x^2 - 6[/tex] on the interval [tex][ 3 , a ][/tex] is [tex]\frac{7a^{2}-63}{a - 3}[/tex]

Formula for finding the average rate of change is given as:

[tex]\frac{f(b) - f(a)}{b - a}[/tex]

Where,

[tex]a=3[/tex]

[tex]f(a) = 7\times3^2 - 6 = 7\times9 -6 =63 - 6 = 57[/tex]

[tex]b = a[/tex]

[tex]f(b) = 7\times a^{2} -6 = 7a^{2} -6[/tex]

Plug in the values into the formula:

Average rate of change = [tex]\frac{f(b) - f(a)}{b - a} = \frac{(7a^{2}-6)- (57)}{a - 3} = \frac{7a^{2}-6- 57}{a - 3} = \frac{7a^{2}-63}{a - 3}[/tex]

Average rate of change = [tex]\frac{7a^{2}-63}{a - 3}[/tex]

Learn more about average rate of change of a function here:

https://brainly.com/question/17085425

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