question_answer 1)

Find the least value of a such that f(x) = x2 + ax + 1 is strictly increasing on (1, 2). 

Answer:

f(x) = x2 + ax + 1             Now 1 < x < 2        2 < 2x < 4        2 + a < 2x + a < 4 + a        2 + a < f?(x) < 4 + a                    ?..(1)       f(x) is strictly increasing on (1, 2), of f?(x) > 0                     [Using (1)]                              Least value of a = ?2.