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Manipal MET2020MathematicsApplication of Derivatives

The values of a , if f(x)=2 e^x-a e^ -x +(2 a+1) x-3 increases x , are in

Options

  1. A[0, )
  2. B(- , 0]
  3. C(- , )
  4. D(1, )

Correct answer

A. [0, )

Step-by-step solution

Given function is f(x)=2 e^x-a e^ -x +(2 a+1) x-3 For increasing function, f(x) 0, x array lr & f^ (x)=2 e^x+a e^ -x +(2 a+1) 0 & (2 e^x+1 )+a (e^ -x +2 ) 0 & a (e^ -x +2 ) - (1+2 e^x ) & a - (1+2 e^x ) (e^ -x +2 ) array array lrl & a & - (1+2 e^x ) (1+2 e^x ) e^x & a & -e^x & e^x (0, ) & -e^x (- , 0) array and a -e^x array ll & a [0, ) array

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