For what values of a is the function f(x) = x | vedclass

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(A) Given the function $f(x) = x^{2} + ax + 1$.To find where the function is increasing,we calculate the derivative:$f'(x) = 2x + a$.The function $f(x

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$a \geq -2$

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(A) Given the function $f(x) = x^{2} + ax + 1$.To find where the function is increasing,we calculate the derivative:$f'(x) = 2x + a$.The function $f(x)$ is increasing on $[1, 2]$ if $f'(x) \geq 0$ for all $x \in [1, 2]$.Since $f'(x) = 2x + a$ is a linear function with a positive slope,its minimum value on the interval $[1, 2]$ occurs at the smallest value of $x$,which is $x = 1$.Therefore,we require $f'(1) \geq 0$:$2(1) + a \geq 0$$2 + a \geq 0$$a \geq -2$.Thus,the function $f(x)$ is increasing on $[1, 2]$ for all $a \geq -2$.

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

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