Question

Is `f(x)=(x+3)(x-6)(x/3-1)` increasing or decreasing at `x=-2`?

Answer 1

`"increasing at "x=-2`

Explanation:

`"To determine if "f(x)" is increasing/decreasing at"`
`"x = -2 differentiate and evaluate at x = - 2"`

`• " if "f'(-2)>0" then "f(x)" is increasing at x = - 2"`

`• " if "f'(-2)<0" then "f(x)" is decreasing at x = - 2"`

`"expanding the factors gives"`

`f(x)=1/3x^3-2x^2-3x+18`

`rArrf'(x)=x^2-4x-3`

`rArrf'(-2)=4+8-3=9>0`

`"Since "f'(-2)>0" then "f(x)" is increasing at x = - 2"`
graph{(x+3)(x-6)(1/3x-1) [-20, 20, -10, 10]}