Question

Is `f(x)=(x^3-6x^2-4x-9)/(x+1)` increasing or decreasing at `x=0`?

Answer 1

Increasing

Explanation:

To find if the function is increasing or decreasing we have to find the slope at `x=0` or calculate the derivative at `x=0`. Let's divide the polynomial first to make it easier. When we divide we get the following
`f(x)=x^2-7x+3-12/{x+1}`

The derivative is then
`f'(x)=2x-7+12/{(x+1)^2}`

Plugging in `x=0` we get
`f'(0)=2(0)-7+12/{(0+1)^2}`
`f'(0)=0-7+12/{1^2}`
`f'(0)=-7+12`
`f'(0)=5`

Since the value is positive, the function is increasing at `x=0`.