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Linear approximation of the 4th root of 17.

A) 1.5

B) 1.7

C) 2.0

D) 2.5

User Ken Liu
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Final answer:

The linear approximation of the 4th root of 17 is 2.03125, which is closest to option D) 2.5.

Step-by-step explanation:

The linear approximation of the 4th root of 17 can be found by using the concept of tangent line approximation. Let's start with a known value, such as the 4th root of 16, which is 2. Then we can calculate the derivative of the function f(x) = x^(1/4) at x = 16, which is f'(x) = 1/(4*x^(3/4)). Plugging in x = 16, we get f'(16) = 1/32. Now we can use the linear approximation formula: f(x) ≈ f(a) + f'(a) * (x - a), where a is 16 and x is 17. Plugging in the values, we get f(17) ≈ 2 + (1/32) * (17 - 16) = 2 + (1/32) = 2.03125. Therefore, the closest option is D) 2.5.

User Tight
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