Across
- 1. the derivative of the quotient of two functions
- 3. the derivative of the product of two functions
- 8. the bounds of a definite integral
- 10. the highest y-value of a function on a given interval
- 16. an integral which is evaluated over an interval used to find the area between a graph and the x-axis
- 20. the value of the derivative at a particular point
- 22. the value that a function approaches as the variable within the function approaches some value
- 23. a method of evaluating if there is a maximum or minimum at a critical point
- 27. the rate of change of the position
- 30. using definite integrals to add the amount of change that has occurred
- 31. a process of finding the maximum or minimum value
- 32. states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]
- 35. When the actual y-value and expected y-value exist and are equal
- 36. the slope of the line tangent to a function commonly written as f'(x)
- 38. states that if a function f(x) is continuous on the closed interval [a, b] and k is a value between f(a) and f(b), then there is a value, x=c, on the interval [a, b] such that f(c)=k.
- 39. the lowest y-value of a function on a given interval
- 40. the curvature of a graph
Down
- 2. An integration method that involves using the chain rule in reverse
- 4. states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b
- 5. the slope of the secant line through two points on the graph of f used in the limit definition of the derivative
- 6. rates of changes related by differentiation
- 7. the derivative of a composition of functions
- 9. a discontinuity where the graph jumps from one piece to another
- 11. A function in which the dependent variable can be written explicitly in terms of the independent variable.
- 12. a line that touches a curve at a point without crossing over
- 13. the x-value where the first derivative equals zero
- 14. a method of evaluating the second derivative at critical values to determine whether there is a relative minimum or maximum
- 15. an interval that includes the endpoints
- 17. the function being integrated or the function that you are taking the antiderivative of
- 18. a hole in the graph
- 19. the point where the function changes concavity
- 21. the antiderivative of a given function
- 24. A function or relation in which the dependent variable is not isolated on one side of the equation.
- 25. a y-value where a maximum/minimum occurs on a sub-interval
- 26. approximation of a definite integral
- 28. a circle whose center is at the origin and has a radius of one
- 29. function whose graph is a horizontal line
- 33. a line that continually approaches a curve without touching it
- 34. approximation of the area under a curve using trapezoids
- 37. the rate of change of the velocity