determine concavity and the x values where points of inflection occur
y=ax^3+bx^2+cx+d
Yeah, I know that I'm looking for whether the graph concaves upward or downward, and the point of inflection is where it changes from one to the other. I started off taking the derivative of the original equation, so I got 3ax^2 + 2bx +c. I'm stuck on what even to do next. We used numbers for all the examples in classes, so I don't know what to do after the first derivative. I can't plug in numbers to determine its concavity, or point of inflection.
For concavity, you're pretty much doing a second derivative test. Remember: a smiley face with pluses for eyes, a frowney face with minus signs for eyes. That'll help you remember what the second derivative tells you. Find out where the second derivative is positive, negative, and where it is zero. Positive = concave up = convex, negative = concave down. Zero is a possible (but not necessarily) point of inflection. To make sure it's a point of inflection, you have to show that the second derivative changes sign there.