Question

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

Answer 1

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`