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# For what values of a the function f given by f (x) is equal to x is raised to 2 plus ax plus 1 is increasing on [1, 2]?

14) For what values of a the function f given by $f (x) = x^2 + ax + 1$  is increasing on
[1, 2]?

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Given function is,
$f (x) = x^2 + ax + 1$
$f^{'}(x) = 2x + a$
Now,  we can clearly see that  for every  value of  $a > -2$
$f^{'}(x) = 2x + a$  $> 0$
Hence, $f (x) = x^2 + ax + 1$   is increasing for every value of   $a > -2$   in the interval [1,2]

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