Question

Is `f(x)=(2x-2)(x+1)(x+4)` increasing or decreasing at `x=1`?

Answer 1

`"increasing at "x=1`

Explanation:

`"to determine if f(x) is increasing/decreasing at x = 1"`
`"evaluate "f'(x)" at x = 1"`

`• " if "f'(1)>0" then f(x) is increasing at x = 1"`

`• " if "f'(1)<0" then f(x) is decreasing at x = 1"`

`"expand the factors to obtain"`

`f(x)=2x^3+8x^2-2x-8`

`rArrf'(x)=6x^2+16x-2`

`rArrf'(1)=6+16-2=20`

`"since "f'(1)>0`

`"then "f(x)" is increasing at x = 1"`
graph{2x^3+8x^2-2x-8 [-10, 10, -5, 5]}