True or false: The derivative of a constant is zero.
TRUE
Fill in the blank: The first derivative indicates _______ of a function.
slope / gradient / instantaneous rate of change
What is the second derivative used for?
To determine the concavity of a function.
Define a polynomial of order 4.
A polynomial of the form ax^4 + bx^3 + cx^2 + dx + e.
What is the derivative of x^4?
4x^3
Find the second derivative of x^3.
6x
True or false: A hyperbola consists of two separate curves.
TRUE
What shape does a hyperbola represent?
Two open curves that extend infinitely.
Define concavity.
The direction of the curvature of a graph.
What does a positive second derivative indicate?
The function is concave up.
What is the derivative of x^2?
2x
What is the derivative of x^4 + 3x^2?
4x^3 + 6x
What is the derivative of 5x^4?
20x^3
True or false: The first derivative can be used to find local maxima.
TRUE
What is the slope of the tangent line at a point?
The value of the first derivative at that point.
What does a negative second derivative indicate?
The function is concave down.
What is the derivative of 3x^3?
9x^2
True or false: The graph of a polynomial is always continuous.
TRUE
