Answer :
The estimated value of f(152.5) is 84.5 is linear approximation.
To estimate the value of f(152.5), we can use the concept of linear approximation.
The linear approximation formula states that if we know the value of a function at a certain point, f(a), and we also know the derivative of the function at that point, f'(a), we can estimate the value of the function at a nearby point, b, by using the equation:
f(b) ≈ f(a) + f'(a)(b - a)
In this case, we are given that f(150) = 82 and f'(150) = 1. We want to estimate f(152.5). Using the linear approximation formula, we have:
f(152.5) ≈ f(150) + f'(150)(152.5 - 150)
Substituting the given values:
f(152.5) ≈ 82 + 1(152.5 - 150)
Simplifying the expression:
f(152.5) ≈ 82 + 1(2.5)
f(152.5) ≈ 82 + 2.5
f(152.5) ≈ 84.5
Therefore, the estimated value of f(152.5) is 84.5.
Learn more about linear approximation from the given link
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