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Linear Approximation?

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Let f(x)=sqrt(x-12) and use the Linear Approximation to this function at a=37 with Δx=0.4 to estimate f(37.4)−f(37)=Δf≈df=
asked Nov 4, 2014 in PRECALCULUS by anonymous

1 Answer

0 votes

Given

f(x) = √(x-12)

Δx = x-x0 = 0.4

f(37) = √(37-12) = √25 = 5

f(37.4) = √(37.4-12) = √25.4

f(x) = √(x-12)

Apply diffenceation.

f '(x) = 1/[2√(x-12)]

Substitute x = 37

f '(37) = 1/[2√(37-12)]

f '(37) = 1/[2√(25)]

f '(37) = 1/(2*5)

f '(37) = 1/10

Formula for Linear Approximation : f(x) = f(x0) + (x-x0)f '(x0)

Consider x = 37.4 and  x0 = 37

f(37.4) = f(37) + (0.4)f '(37)

Substitute f '(37) = 1/10

f(37.4) = f(37) + (0.4)(1/10)

f(37.4) - f(37) = 0.04

The solution is f(37.4) - f(37) = 0.04

answered Nov 4, 2014 by lilly Expert
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