# Maths

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f(x)is a function differentiable at x=1 and f'(1)=1/8.
what is the value of f(x)-f(1)

f'(x) denotes the derivative of f(x)

• Maths -

For x near 1, you can use linearlization, which is
f(x)=f'(1)(x-1)+f(1)
=(1/8)x+f(1)
Therefore, within the errors of the linearization,
f(x)-f(1) = (x-1)/8 (approximately)

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