# How do you locate the critical points of the function #f(x) = x^3 - 15x^2 + 4# and use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither?

##### 1 Answer

Critical point: number

**Finding Critical Points**

Both

**Testing Critical Points**

The second derivative of

At the critical point

The second derivative test (for local extrema) tells us that,

At the critical point

The second derivative test (for local extrema) tells us that,

And here's the graph (you'll have to zoom to see details):

graph{y=x^3-15x^2+4 [-16, 41.74, -19.96, 8.92]} #