A community for students.
Here's the question you clicked on:
 0 viewing
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).
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).

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me try to do it on my own,tell me if i'm doing something wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember, use the information that f(2)=8, to find f(2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439294446810:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hmm, you don't need that graph at all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay i have no idea where to start :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Look at the middle line segment, going from (2,2,) to (2,2) is the line segment you need to look at

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay is the answer 8?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im saying 8 only because the graph seems mirrored and if it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Idk, 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
 one year ago
Best ResponseYou've already chosen the best response.0okay that seems way better, one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Good, 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
 one year ago
Best ResponseYou've already chosen the best response.0yes!! y=x \[f(2)=8\int\limits_{2}^{2}x.dx\] Now it's a simple matter of integration

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Hey! allternatively we could also use the symmetry to conclude that the integral is 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0_ how did i not see that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yeah, the same amount of area under the line is negative as it is positive so it cancels out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh well it doesn't matter i get it! :D

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439295272579:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but it is also important that you know the method

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much guys, i should probably head to bed its 5:20 am here

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyway thanks again!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Another alternative, Since \(f'(x)\) is an odd function, it follows that \(f(x)\) is an even function. Therefore \(f(2)=f(2)=8\)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.