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Calculus

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Find the local linearization of g(x)=sqrt 4x near x=2
use local linearization to estimate g(2.05)
is your estimate too high or too low?

  • Calculus -

    g(x) = sqrt 4x = 2 sqrtx
    Local linearization near x = 2:
    gl(x)= g(x=2) + [dg/dx@x=2])*(x-2)g
    g(x=2) = 2 sqrt2
    dg/dx = 2(1/2)/sqrtx = 1/sqrtx
    dg/dx @ x=2 = 1/sqrt2
    gl(x) = 2sqrt2 + (1/sqrt2)(x-2)
    is the linearization about x = 2
    For x = 2.05,
    g(2.05) = 2.86356
    The linearized approximation is
    gl(2) + (0.05)/1.41421
    = 2.8284 + 0.0353 = 2.86376

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