Question

Is `f(x)=(x-4)(x-12)(x/4-1)` increasing or decreasing at `x=-1`?

Answer 1

`f(x)" is increasing at " x=-1`

Explanation:

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

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

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

`"expand factors of f(x)"`

`f(x)=(x^2-16x+48)(x/4-1)`

`color(white)(f(x))=1/4x^3-5x^2+28x-48`

`"differentiate using the "color(blue)"power rule"`

`f'(x)=3/4x^2-10x+28`

`f'(-1)=3/4+10+28>0`

`rArrf(x)" is increasing at x = - 1"`