Question

Find the intervals of increase and decrease of $f\left(x\right)=6x^2+x-2$

Answer 1

$f\left(x\right)=6x^2+x-2$

For function to be increasing $f^{\prime }\left(x\right)>0$

$f^{\prime }\left(x\right)=12x+1>0$

$12x>-1$

$x>-1/12$

$xϵ(\frac{-1}{12},\infty )$

For function to be decreasing, $f^{\prime }\left(x\right)<0$

$12x+1<0$

$12x<-1$

$x<\frac{-1}{12}$

$xϵ(-\infty ,\frac{-1}{12})$