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find g(-1) and g''(-1)

Mathematics
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|dw:1356718690979:dw|
\[g(x)=\int\limits_{0}^{x}f(t) dt\]
graph above is f

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Other answers:

|dw:1356718836761:dw|
find g(-1)
can u find the point of intersection of those 2 lines ? or, equation of those lines ??
Is g(x) a constant? I don't see x in the definition of g(x). Does f(x) = 0 for x>2, or does it decrease forever?
i know that f'(-1)=0
what i have no idea how to find the f(-1)
|dw:1356720077842:dw|
slope is 3
  • hba
Now you can find the equation :)
and u also have point , so equation is ?
y=3x+3
x=-1 thats your f(t) for 0 to -1
\(g(-1)=\int\limits_{0}^{-1}(3x+3) dt\)
can u find g(-1) now
yes
good :)
  • hba
-(3x+3)
-3/2
what about f''(-1)
u sure about -3/2 ??
yes
|dw:1356720626985:dw|
ok, \(g'(x)=(d/dx)\int_0^xf(t)dt = f(x)\\so,g''(x)=f'(x)\\g"(-1)=f(-1)\) can u find f(-1) ?? and no
why not
why ?
why u want to use that line ?? f(-1) is simple..
ok
0
yes, correct.

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