## anonymous 4 years ago Let f(x)=5x^2. Find a value A such that the average rate of change of f(x) from 1 to A equals 60.

1. amistre64

the average rate of change is just (f(A) - f(1))/(A-1)

2. anonymous

i know!

3. anonymous

im getting the wrong answer for some reason though

4. anonymous

and im getting frustrated

5. amistre64

$\frac{5a^2-5.1^2}{a-1}=60$ $5a^2-5=60(a-1)$ $5a^2-5=60a-60$ $5a^2-60a-5+60=0$ $5(a^2-120a+11)=0$

6. anonymous

5.1?

7. amistre64

$a=\frac{1}{2}(12\pm\sqrt{12^2-4(11)})$

8. amistre64

its easier for me to get to the . then the *

9. myininaya

$\frac{5a^2-5(1)^2}{a-1}=60=> \frac{5(a^2-1)}{a-1}=60$ $=>\frac{5(a-1)(a+1)}{a-1}=60 => 5(a+1)=60=> a+1=12$

10. amistre64

pfft!! thats cheating, and only gets one of them :)

11. anonymous

ITS 11!!!!!!!!!!!!!!! O MY GOD!!!!!!!!!!!!!!!!!!!!!!!!

12. amistre64

144-44 = 100 sqrt100 = 10 12 +- 10 /2 /2 6 +- 5 = 1 and 11?

13. amistre64

cant be 1 so that leaves 11, yeah

14. myininaya

a cannot be 1 dear lol

15. myininaya

lol

16. amistre64

i was getting to that :)

17. myininaya

so my way gets all the possible values of A lol

18. amistre64

not the complex ones :P

19. myininaya

shhh lets not go there lol