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]} #