question_answer 65)

Find the maximum and minimum values, if any of the following functions given by : (i) f(x) = (2x – 1)2 + 3 (ii) f(x) = 9x2 + 12x + 2 (iii) f(x) = – (x – 1)2 + 10 (iv) g(x) = x3 + 1  

Answer:

 (I) f(x) = (2x ? 1)2 + 3        f(x)  Minimum value of f(x) = 3 and maximum value of f(x) does not exist. (II)    f(x) = 9x2 + 12x + 2                                      Min, f(x) = ?2 and       Max. f(x) does not exist. (III)   f(x) = ? (x ? 1)2 + 10 = 10 ? (x ? 1)2                   Min. f(x) does not exist. (IV)  f(x) = x3 + 1              is an increasing function therefore extremum values of f(x) does not exist.