Question

Is `f(x)=(x^3-4x^2-2x-4)/(x-1)` increasing or decreasing at `x=2`?

Answer 1

Increasing.

Explanation:

Express the ratio in the quotient remainder form
`x^2-3x-5-9/(x-1)`
`f' = 2x-3 + 9/(x-1)^2`.
At x = 2, f' = 10 > 0.
So, f is increasing at x = 2.