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AP EAMCET202319 May 2023Morning ShiftMathematicsApplication of DerivativesActual

Let f : R R be a continuous function. If px + my + n =0 is a tangent drawn to the curve y=f(x) at x= , then at x=0, d d x (f ( e^ 2 x ) )=

Options

  1. A0
  2. Bp m
  3. C-2 m p
  4. D-2 p m

Correct answer

D. -2 p m

Step-by-step solution

Since p x+m y+n=0 is tangent drawn to the curve y=f(x) at x= . Hence d y d x =f^ (x)=( Slope of p x+m y+n=0) d f( x ) d x = ( -p m ) f(x)= -p m x+c when x= e^2 x then (where c = arbitrary constant) f ( e^ 2 x )= -p m ( e^ 2 x )+c Hence d d x [f ( e^ 2 x ) ]=- p m d d x (e^ 2 x )+ d c d x Hence d d x [f ( e^ 2 x ) ]= -2 p m e^ 2 x when x=0 , then d d x [f ( e^ 2 x ) ]= -2 p m e^0= -2 p m

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