Is #f(x)=(x-3)(x+3)(x-2)# increasing or decreasing at #x=1#?
Decreasing. Instantaneous rate of change -10
To find if the function is decreasing, we need the first derivative. The easiest way to do this is to expand into the cubic and then use the power rule:
Taking the derivative:
This "function" tells us the slope at x. So, plug in x=1: