Question

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

Answer 1

Decreasing

Explanation:

Original equation :
`f(x)=(x+1)(x-4)(x-2)`

foil:
`f(x)=(x^2-3x-4)(x-2)`
`f(x)=(x^3-5x^2+2x+8)`

Derive:
`f^'(x)=(3x^2-10x+2)`

Plug in x:
`f^'(1)=(3(1)^2-10(1)+2)`
`f^'(1)=(3-10+2)`
`f^'(1)=(-5)`

`f^'(1)` is negative, so `f(x)` is decreasing at `x=1`