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Answer :
based on the linear approximation, we can estimate that f(146) is approximately equal to 78.
To estimate f(146) based on the given information, we can use the concept of linear approximation.
Linear approximation assumes that for small changes in x, the change in f(x) is approximately proportional to the change in x. Mathematically, we can express this as:
Δf ≈ f'(a) * Δx
where Δf represents the change in f(x), f'(a) is the derivative of f(x) evaluated at a, and Δx is the change in x.
In this case, we want to estimate f(146) based on the known values at x = 150. So, let's calculate the change in x:
Δx = 146 - 150 = -4
Now, we can use the linear approximation formula:
Δf ≈ f'(150) * Δx
Δf ≈ 1 * (-4) = -4
To estimate f(146), we need to add the change in f to the value of f(150):
f(146) ≈ f(150) + Δf
f(146) ≈ 82 + (-4)
f(146) ≈ 78
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