12th Class Mathematics Continuity and Differentiability

  • question_answer 146) Find the absolute maximum value and minimum value of the following functions in the given intervals: I.      f(x) = x3, II.     f(x) = sin x + cos x, III.    f(x) = 4x  IV.   f(x) = (x ? 1)2 + 3x           

    Answer:

    f(x) = x3,               f?(x) = 0             x = 0

          x -2 0 2
    f(x) -8 0 8
           Absolute maximum value of f?(x) = 8 at x = 2 and absolute minimum value of f(x) = ?8 at x = ?2. II.     f(x) = sin x + cos x,                        
          x 0
    f(x) 1 -1
     About maximum value of f(x)  and absolute minimum value of f(x) ?1 at x = III.             f?(x) = 0
    x ?2 4 9/2
    f(x) ?10 8 63/8
     f(x) have absolute maximum value = 9 at x = 4 and absolute minimum value = ? 10 at x = ?2. IV. f(x) = (x ? 1)2 + 3,                                            
    X ?3 1
    f(x) 19 3
     f(x) have absolute maximum value = 19 at x = ?3 and absolute minimum value = 3 at x = 1.  


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