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MHT CET202525 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The angle , at which the curves y =3^x and y =7^x intersect, is given by

Options

  1. A= ( 3 7 ) 1+( 3)( 7)
  2. B= (7 ) 1+( 3)( 7)
  3. C= ( 3 7 ) 1-( 3)( 7)
  4. D= ( 7 3 ) 1-( 3)( 7)

Correct answer

A. = ( 3 7 ) 1+( 3)( 7)

Step-by-step solution

The curves y = 3^x and y = 7^x intersect when 3^x = 7^x . This equality holds only at x = 0 , yielding the intersection point (0,1) . The derivatives are dy dx = 3^x 3 and dy dx = 7^x 7 . At x = 0 , the slopes are m₁ = 3 and m₂ = 7 . The angle between the curves satisfies = m₁ - m₂ 1 + m₁ m₂ . Substituting gives = 3 - 7 1 + ( 3)( 7) = ( 3 7 ) 1 + ( 3)( 7) , which corresponds to option A . The answer is A .

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