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AP EAMCET202125 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If y=5 x^2+6 x+6, x=2 and x=0.00 l , then the values of y and d y respectively are

Options

  1. A0.026 and 0.026005
  2. B0.026005 and 0.026
  3. C0.026005 and 0.26
  4. D0.0026 and 0.026

Correct answer

B. 0.026005 and 0.026

Step-by-step solution

If y=5 x^2+6 x+6, x=2 and x=0.001 array rlrl & d y d x & =10 x+6 & d y & = ( d y d x ) x d y & =10 x x+6 x & =10 2(0.001)+6(0.001) & & d y & =0.026 & y & =5 x^2+6 x+6 array aligned & If y=f(x) , then y=f(x+ x)-f(x) & y= 5(x+ x)^2+6(x+ x)+6 - 5 x^2+6 x+6 & =5 x^2+5( x)^2+10 x x+6 x+6 x+6 & -5 x^2-6 x-6 & y=5 (0.001)^2+10 2 (0 001)+6(0 001) & y=0 000005+0 020+0 006 & y=0 026005 & aligned

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