MHT CET202522 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

The approximate value of [3] 64 04 is

Options

A4 00043
B4 00076
C4 00083
D4 00064

Correct answer

C. 4 00083

Step-by-step solution

Approximating the cube root of 64.04 using linear approximation with f(x) = x^ 1/3 . Since 64.04 = 64 + 0.04 , let a = 64 where f(64) = 4 and h = 0.04 . The derivative f'(x) = 1 3 x^ -2/3 , so f'(64) = 1 3 64^ 2/3 = 1 3 16 = 1 48 . Applying the approximation gives: [3] 64.04 4 + 0.04 1 48 = 4 + 0.04 48 = 4 + 1 1200 4.000833 This value corresponds to option C.

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