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AP EAMCET201825 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

The curve f ( x ) = e x sin x is defined in the interval [ 0 , 2 π ] . The value of x for which the slope of the tangent drawn to the curve at x is maximum, is

Options

  1. Aπ 4
  2. Bπ 2
  3. Cπ 6
  4. Dπ 3

Correct answer

B. π 2

Step-by-step solution

Given: f ( x ) = e x sin x We know that the slope of tangent is given by d y d x = f ' x . Now, f ' ( x ) = Z = e x sin x + e x cos x Z = e x sin x + cos x d Z d x = e x sin x + cos x + e x cos x - sin x ⇒ d Z d x = 2 e x cos x For maxima, d Z d x = 0 ⇒ 2 e x cos x = 0 ⇒ e x cos x = 0 ∵ e x ≠ 0 ,   x ∈ R ∴ cos x = 0 ⇒ x = π 2 ,   3 π 2 ;   ∵ x ∈ 0 , 2 π   Now, ⇒ d 2 Z d x 2 = 2 e x cos x - 2 e x sin x = 2 e

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