Question

Find the minimum value of a, such that function $f\left(x\right)=x^2+ax+5$, is increasing in interval $[1,2]$.

Answer 1

$\begin{array}{c}f\left(x\right)=x^{2}ax+5\\ differentiatewithrespecttox\\ \Rightarrow f\left(x\right)=2x+a\\ \Rightarrow f\left(x\right)>0\\ \Rightarrow 2x+a>0\\ a>-2x\\ Putx-1\\ \therefore minimumvalueofis-2\times 1=-2\end{array}$