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NathanJHW
 one year ago
Given that f (−0.5) = 2 and f ′(−0.5) = 4 , using a tangent line approximation you would estimate f (0) to be:
NathanJHW
 one year ago
Given that f (−0.5) = 2 and f ′(−0.5) = 4 , using a tangent line approximation you would estimate f (0) to be:

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whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0Do you understand what that all means?

perl
 one year ago
Best ResponseYou've already chosen the best response.2You 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

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0The 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
 one year ago
Best ResponseYou've already chosen the best response.2you can also solve this using delta y ≈ f ' (x) * delta x

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433289725823:dw

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0we estimate f(b) as (ba) * f'(a)+ f(a)
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