Across
- 4. problem that involves two or more quantities and their corresponding rates of change with respect to time; by knowing how the variables are related, and how fast one of them is changing, then how fast the other one is changing can be determined
- 10. a function in one variable such that its derivative exists at each point in its entire domain; no cusps, corners, discontinuity, or vertical tangents on the graph of the function
- 11. a line that touches a curve at only one point; the slope of this is equal to the derivative of a function
- 12. formula for computing the derivative of the composition of two or more functions; if f is a function and g is a function, then it expresses the derivative of the composite function f ∘ g in terms of the derivatives of f and g
- 13. relates to the rate of change of a function's derivative and describes the way it is changing; concave up when f' is increasing and concave down when decreasing
- 17. a function whose graph has no breaks or holes; if a function meets the following: (1) f(c) is defined (2) limit of f(x) exists (3) limit of f(x) is c
- 18. a line that a graph follows closely but never touches; a line that a curve approaches, as it heads towards infinity
- 19. equal to the area under a graph of a function for some interval; also known as the antiderivative
Down
- 1. the derivative of velocity with respect to time; helps determine whether an object is speeding up or slowing down
- 2. the value that a function approaches as the input gets closer to some value; the value that approached but never quite reached
- 3. statement that can be demonstrated to be true by accepted mathematical operations; types include Mean Value, Intermediate, Rolle's, etc.
- 5. any point at which the value of a function is largest (a maximum) or smallest (a minimum); there are two types: absolute and relative/local
- 6. slope of a line tangent to a function; the rate of change of a function with respect to a variable
- 7. a point in which the graph is not continuous; types include jump, removable, infinite, and oscillating
- 8. where the function changes concavity; uses the second derivative test to determine if f''(x) = 0
- 9. an approximation of a region's area, obtained by adding up the areas of multiple simplified slices of the region; types include: right endpoint, left endpoint, midpoint, and trapezoidal
- 12. a point on a graph in which the derivative of a function is 0 or undefined; if x is in the domain of the function and either f′(x) = 0 or f′(x) does not exist (all relative maxima and minima are this)
- 14. rule that helps find limits when direct substitution ends with the indeterminate forms 0/0 or ∞/∞; states that a limit can be found by differentiating the numerator and the denominator
- 15. derivative of the position and integral of acceleration; the rate and direction of an object's movement
- 16. the integral of velocity; tells where an object is at a point in time