Question

Let f(x)=(x−6)2
. Find the average rate of change of f(x) with respect to x from x=a to x=a+h if h≠0

Answer 1

\[\frac{f(x_1)-f(x_0)}{x_1-x_0}\]
Just use the formula for slope

Answer 2

ummm how would that end up giving me the right answer? isnt there more to the problem?

Answer 3

im still just really confused haha

Answer 4

you are given x_1=a and x_0=a+h

Answer 5

okay...

Answer 6

can you show me the step by step way on how to do this please? It would help me a lot :) I'm sorry im not not fully understanding it

Answer 7

we plug in

Answer 8

\[\frac{f(a)-f(a+h)}{a-(a+h)}\]

Answer 9

so is that the final answer?

Answer 10

no we have to replace f(a) with (a-6)^2
and f(a+h) with (a+h-6)^2

Answer 11

Then simplify using algebra

Answer 12

You will probably have to multiply some stuff out

Answer 13

\[\frac{(a-6)^2+(a+h-6)^2}{a-(a+h)}\]
Can you play with this and simplify?

Answer 14

oops I type-o
\[\frac{(a-6)^2-(a+h-6)^2}{a-(a+h)}\]

Answer 15

I will show you a trick that might be helpful:
\[(a+h-6)^2=(a+h-6)(a+h-6)=([a-6]+[h])([a-6]+[h]) \]
\[=(a-6)^2+2(a-6)h+h^2 =a^2-12a+36+2a-12+h^2\]

Answer 16

Thank you!