Question

Is `f(x)=3x^3-2x^2` increasing or decreasing at `x=0`?

Answer 1

Neither

Explanation:

Differentiate the expression to find the gradient, then substitute `x=0` into the result. If that is negative the function is decreasing and if it is positive it is increasing. If it is zero, it is an inflection point.

`d/dxf(x) = 9x^2 -4x`

At `x=0` this equals zero, and therefore the function is neither increasing nor decreasing.