How do you estimate Δf = f (a + Δx) - f (a) using the Linear Approximation given #f(x) = x – 4x^2#, a = 1, Δx = -0.3?

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Answer 1 · 2017-08-01T06:43:20

The value of #Deltaf=2.1#

The linear approximation is

#f(a+Deltax)=f(a)+f'(a)*Deltax#

Here,

#a=1#

#Deltax=-0.3#

#f(x)=x-4x^2#, #=>#, #f'(x)=1-8x#

Therefore,

#f(a+Deltax)=f(a)+f'(a)*Deltax#

#f'(1)=1-8*1=-7#

#f(1-0.3)=f(1)-(-7)*0.3=f(1)+2.1#

#Deltaf=f(1-0.3)-f(1)=2.1#