Is ##f(x)=3x^2-x+4## increasing or decreasing at ##x=2##?

Given

##f(x)=3x^2-x+4##

Diffrentiating w.r to x we get

##f'(x)=d/(dx)(3x^2-x+4)##

##=>f'(x)=6x-1+0##

for ##x=2##

##=>f'(2)=6*2-1=11>0##

As ##f'(2)>0## i.e.the slope at ##x=2## is ##+ve## ,the function ##f(x)## is increasing at ##x=2##