AP EAMCET202022 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

What is the value of [3] 26 corrected up to three decimal places?

Options

A2.998
B2.844
C2.962
D2.823

Correct answer

C. 2.962

Step-by-step solution

Let y=f(x)=x^ 1 / 3 aligned x+ x & =26 27+ x & =26 [ let x=27] aligned x=-1 We have, y=x^ 1 / 3 Differentiate w.r.to ' x ' aligned d y d x & = 1 3 x^ 1 3 -1 d y & = 1 3 x^ - 2 3 d x d y & = 1 3 x^ 2 / 3 d x= 1 3 .(27)^ 2 3 (-1) y & = -1 3(9) =- 1 27 -0.037 3 26 & =y+ y=3+(-0.037)=2.962 aligned Hence, option (3) is correct.

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