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BITSAT2015MathematicsApplication of DerivativesActual

The slope of the tangent to the curve y=e^ x cos x is minimum at x= , 0 a 2 , then the value of is

Options

  1. A0
  2. B2
  3. C3 2

Correct answer

B. 2

Step-by-step solution

Let m be the slope of the tangent to the curve y=e^ x x Then, m= d y d x =e^ x ( x- x) Diff. w.r.t 'x' array r dm dx = e ^ x ( x - x )+ e ^ x (- x - x ) =-2 e ^ x x array and d ² ~m dx ² =-2 e ^ x ( x + x ) Put dm dx =0 x =0 x =0, , 2 Clearly, d ² ~m dx ² >0 for x = Thus, y is minimum at x= . Hence the value of =

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