## anonymous 4 years ago Let g(x)=2x^2+2x+1. Find the value of c between 1 and 3 such that the average rate of change of g(x) from x=1 to x=3 is equal to the instantaneous rate of g(x) at x=c.

1. anonymous

do just plug in 1 and 3 and do the rate of change and then plug in x and c and do the same?

2. myininaya

so do this $g'(c)=\frac{g(3)-g(1)}{3-1}$

3. anonymous

ok i get 10 doing that

4. myininaya

Have you plugged into the formula I gave you?

5. myininaya

find g' then find g'(c) and set that equal to the slope of the secant line from x=3 to x=1

6. anonymous

you're losing me lol

7. myininaya

do you know hot to find g'?

8. anonymous

4x + 2

9. anonymous

and then plug in 1 and 3?

10. myininaya

$4c+2=\frac{g(3)-g(1)}{3-1}$

11. anonymous

ok so the answer is 2

12. anonymous

thanks

13. myininaya

$4c+2=\frac{2(3)^2+2(3)+1-[2(1)^2+2(1)+1]}{2}$

14. anonymous

ok i have another similar prob that i need help with... ill post it on the main thing