## anonymous one year ago The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(2) = 8, evaluate f(–2).

1. anonymous

2. anonymous

let me try to do it on my own,tell me if i'm doing something wrong

3. anonymous

Sure

4. anonymous

Remember, use the information that f(2)=8, to find f(-2)

5. anonymous

|dw:1439294446810:dw|

6. anonymous

that feels wrong

7. anonymous

Hmm, you don't need that graph at all

8. anonymous

okay i have no idea where to start :/

9. anonymous

Look at the middle line segment, going from (-2,-2,) to (2,2) is the line segment you need to look at

10. anonymous

11. anonymous

im saying 8 only because the graph seems mirrored and if it

12. anonymous

Idk, I haven't calculated the answer yet use the formula $\int\limits_{-2}^{2}f'(x)dx=f(2)-f(-2)$ $f(-2)=f(2)-\int\limits_{-2}^{2}f'(x)dx=8-\int\limits_{-2}^{2}y.dx$ Have you studied about the definite integral?

13. anonymous

okay that seems way better, one sec

14. anonymous

and yes i have

15. anonymous

Good, you need to find y(x) for the interval -2 to 2, it will be the equation of the middle line segment, again since it's passing through origin it's c will be 0 $y=mx+c=mx+0=mx=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}})x$ m=slope (x1,y1) (x2,y2) are any points on the line segment

16. anonymous

x

17. anonymous

so y = x?

18. anonymous

yes!! y=x $f(-2)=8-\int\limits_{-2}^{2}x.dx$ Now it's a simple matter of integration

19. anonymous

8!!

20. anonymous

I LOVE YOU!!

21. ganeshie8

Hey! allternatively we could also use the symmetry to conclude that the integral is 0

22. anonymous

good job jeb!!

23. anonymous

-_- how did i not see that

24. anonymous

Oh yeah, the same amount of area under the line is negative as it is positive so it cancels out

25. anonymous

oh well it doesn't matter i get it! :D

26. ganeshie8

|dw:1439295272579:dw|

27. anonymous

but it is also important that you know the method

28. anonymous

thanks so much guys, i should probably head to bed its 5:20 am here

29. anonymous

anyway thanks again!

30. ganeshie8

Another alternative, Since $$f'(x)$$ is an odd function, it follows that $$f(x)$$ is an even function. Therefore $$f(-2)=f(2)=8$$

31. anonymous

amazing