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QUESTION
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##
