or a minimum.
12(0)^2 + 12(0) − 4 = −4This is negative, so the curve has a maximum at (0, 1); the curve is concave down there.
This is positive, so the curve has a minimum at ; the curve is concave up there.
12(−2)^2 + 12(−2) − 4 = 20
This is positive, so the curve has a minimum at (−2, −7) and the curve is also concave up there.
We can now plot the graph.
Finding a Cusp
If the derivative of a function approaches ∞ from one side of a point and −∞ from the other, and if the
function is continuous at that point, then the curve has a “cusp” at that point. In order to find a cusp, you
need to look at points where the first derivative is undefined, as well as where it’s zero.