Use an appropriate local linear approximation to estimate the value of √36.03.
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Answer:
√36.03 ≈ 6.0025 (approx)
Step-by-step explanation:
Let f(x) = √x.
The derivative is f '(x) = 1 / 2√x.
A linear approximation near x (so for small h) is given by
f '(x) ≈ [ f(x+h) - f(x) ] / h
=> f(x+h) = f(x) + h f '(x)
Putting x = 36 and h = 0.03 gives
√36.03
= f(36 + 0.03)
≈ f(36) + 0.03 f '(36)
= √36 + 0.03 / 2√36
= 6 + 0.03 / 12
= 6 + 0.01 / 4
= 6 + 0.0025
= 6.0025
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