NathanJHW
  • NathanJHW
Given that f (−0.5) = 2 and f ′(−0.5) = 4 , using a tangent line approximation you would estimate f (0) to be:
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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NathanJHW
  • NathanJHW
0 1 –2 –3 4
whpalmer4
  • whpalmer4
Do you understand what that all means?
NathanJHW
  • NathanJHW
Not really.

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More answers

perl
  • perl
You can use the equation of a line to make your 'linear approximation' . y - y1 = m( x - x1) Suppose x1 = -0.5 y1 = f(-0.5)= 2 m = f ' (-0.5)=4 We have y - 2= 4 ( x - (-.5)) y = 4( x + .5) + 2 now plug in x = 0
NathanJHW
  • NathanJHW
y=2
NathanJHW
  • NathanJHW
y=4 sorry
whpalmer4
  • whpalmer4
The tangent line gives us the slope of the curve at that very point. So if we know the value of our function somewhere nearby, and the slope of the tangent line at that point nearby, we can estimate the value of the function at our point of interest.
perl
  • perl
you can also solve this using delta y ≈ f ' (x) * delta x
whpalmer4
  • whpalmer4
|dw:1433289725823:dw|
whpalmer4
  • whpalmer4
we estimate f(b) as (b-a) * f'(a)+ f(a)

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