Questions and Answers
What is the effect of a > 0 on the graph of y = ax^3 + bx^2 + cx + d?
How do you find the y-intercept of a cubic function f(x) = ax^3 + bx^2 + cx + d?
What is the purpose of finding the first derivative f'(x) when sketching a cubic graph?
What is a point of inflection in a cubic graph?
Signup and view all the answers
What is the condition for a graph to be concave up?
Signup and view all the answers
How can you determine the shape of a cubic graph?
Signup and view all the answers
What is a local minimum in a cubic graph?
Signup and view all the answers
What is the first step in the general method for sketching cubic graphs?
Signup and view all the answers
What happens to the graph of y = ax^3 + bx^2 + cx + d when a < 0?
Signup and view all the answers
What is the purpose of solving f(x) = 0 when finding the intercepts of a cubic function?
Signup and view all the answers
What is the relation between the concavity of a curve and its gradient?
Signup and view all the answers
What is the condition for a point to be a local maximum in a cubic graph?
Signup and view all the answers
What do you need to find to determine the x-coordinates of the stationary points of a cubic function?
Signup and view all the answers
What happens at a point of inflection in a cubic graph?
Signup and view all the answers
What is the purpose of finding the x-intercepts when sketching a cubic graph?
Signup and view all the answers
What is the relation between the sign of a and the orientation of a cubic graph?
Signup and view all the answers
If a > 0, what is the relationship between the x-intercepts and the y-intercept of a cubic graph?
Signup and view all the answers
What is the relation between the stationary points and the local maximum and local minimum?
Signup and view all the answers
What is the purpose of finding the x-coordinates of the stationary points?
Signup and view all the answers
What is the relationship between the concavity of a curve and its gradient?
Signup and view all the answers
How can you determine the orientation of a cubic graph?
Signup and view all the answers
What is the condition for a graph to change concavity?
Signup and view all the answers
What is the purpose of finding the second derivative f''(x) when sketching a cubic graph?
Signup and view all the answers
How can you determine whether a stationary point is a local maximum or local minimum?
Signup and view all the answers