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

##### 1 Answer

Decreasing; see explanation

#### Explanation:

In order to determine the solution, we must find the derivative

The Quotient Rule states that, for

In this case, we have via the power rule:

Thus:

We can simplify further if we wish, but for the purposes of this problem it's unnecessary.

Now find

Because the derivative is negative at this point,

Viewing the graph below, we can verify this is correct.

graph{(3x^3 + 3x^2 + 5x + 2)/(x-2) [-2.947, 9.2, 121.787, 127.86]}