Question

Is `f(x)=(3x^3+x^2-2x+7)/(2x-2)` increasing or decreasing at `x=3`?

Answer 1

`f'(3)=79/8>0`

Explanation:

By the Quotient rule we get
`f'(x)=((9x^2+2x-2)*(2x-2)-(3x^3+x^2-2x+7)*2)/(2x-2)^2`
Simplifying we get

`f'(x)=1/2*(6x^3-8x^2-2x-5)/(x-1)^2`