Question

Is `f(x)=(-5x^3-x^2+2x-2)/(-x+3)` increasing or decreasing at `x=1`?

Answer 1

Decreasing

Explanation:

`f(x) = (5x^3+x^2-2x+2)/(x-3)`

`f'(x) = ((15x^2+2x-2)(x-3)-(5x^3+x^2-2x+2)(1))/(x-3)^2`

`f'(1) = ((15+2-2)(-2)-(5+1-2+2))/(-2)^2 = (-30-6)/4 < 0`