Question

Prove that $f\left(x\right)=x^2$ is increasing in interval $(0,\infty )$ and decreasing in interval $(-\infty ,0)$.

Answer 1

$\begin{array}{c}f\left(x\right)=x^2\\ differentiatew.r.tox\\ f\left(x\right)=2x\left[\because dy/dx{f}^{\prime }\left(x\right)\right]\\ forincreasing\\ f^{\prime }\left(x\right)>0\\ 2x>0\\ x>0\\ andfordecreasing\\ f^{\prime }\left(x\right)<0\\ 2x<0\\ x<0\\ \left(-\infty /0\right)Ans.\end{array}$