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AP EAMCET201921 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

If f(x)=(2 k+1) x-3-k e^ -x +2 e^x is monotonically increasing for all x R , then the least value of k is

Options

  1. A1
  2. B0
  3. C- 1 2
  4. D-1

Correct answer

B. 0

Step-by-step solution

Given, f(x)=(2 k+1) x-3-k e^ -x +2 e^x Since, f(x) is monotonically increasing for all x R . So, array rlrl & & (2 k+1)+k e^ -x +2 e^x & 0 & e^ -x ((2 k+1) e^x+k+2 e^ 2 x ) & 0 or & (2 k+1) e^x+k+2 e^ 2 x & 0 & 2 e^x (e^x+k )+1 (e^x+k ) & 0 & & (2 e^x+1 ) (e^x+k ) & 0 & & e^x+k 0 or k & 0 array Hence, least value of k is zero.

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