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MHT-CET : Mathematics Entrance Exam

MHT - CET : Mathematics - Application of Derivatives Formulae Page 1

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1.Equation of tangent in terms of slope

 

y - f (a) = f '(a) (x - a)

 

2. Formula for Approximation

 

f (a + h) f (a) + h f '(a)

 

3. Formulae for Error

 

  • if y = f(x) and dx is an error x then error in y, dy   

dy

dx

. dx

 

 

  • Relative error in y   is 

dy

y

 

 

  •  Percentage error in y   is  

dy

y

   100

 

4. Maxima and Minima

 

  • First Derivative Test:
    y = f(x) has maximum value at x = c if
       (i)
    f ' (c - h) > 0
       (ii)
    f ' (c) = 0 and
       (iii)
    f ' (c + h) < 0

    y = f(x) has minimum value at x = c if
        (i)
    f ' (c - h) < 0
       (ii)
    f ' (c) = 0 and
      (iii)
    f ' (c + h) > 0
  • Second Derivative Test:
    y = f(x) has maximum value at x = c if
      (i)
    f ' (c) = 0 and
      (ii)
    f '' (c) < 0

    y = f(x) has minimum value at x = c if
      (i)
    f ' (c) = 0 and
      (ii)
    f '' (c) > 0

 

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