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

- anonymous

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

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- anonymous

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- anonymous

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

- anonymous

Sure

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## More answers

- anonymous

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

- anonymous

|dw:1439294446810:dw|

- anonymous

that feels wrong

- anonymous

Hmm, you don't need that graph at all

- anonymous

okay i have no idea where to start :/

- anonymous

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

- anonymous

okay is the answer 8?

- anonymous

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

- 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?

- anonymous

okay that seems way better, one sec

- anonymous

and yes i have

- 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

- anonymous

x

- anonymous

so y = x?

- anonymous

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

- anonymous

8!!

- anonymous

I LOVE YOU!!

- ganeshie8

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

- anonymous

good job jeb!!

- anonymous

-_- how did i not see that

- anonymous

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

- anonymous

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

- ganeshie8

|dw:1439295272579:dw|

- anonymous

but it is also important that you know the method

- anonymous

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

- anonymous

anyway thanks again!

- ganeshie8

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

- anonymous

amazing

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