Across
- 3. uv` + vu`
- 5. An equation involving two or more variables that are differentiable functions of time that can be used to find an equation that relates the corresponding rates.
- 7. The slope of the tangent line at a point on the curve.
- 15. The greatest y-value that a function achieves.
- 17. Where the derivative changes signs from positive to 0 to negative.
- 22. A rectangular sum of the area under a curve where the domain is divided into subintervals and the height of each rectangle is the function value at the midpoint of the subinterval.
- 24. A point or value of the independent variable at which the value of a function is not equal to its limit as the value of the independent variable approaches that point, or where it is not defined.
- 25. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point.
- 29. The expression for the evaluation of the indefinite integral of a positive function between two limits of integration.
- 31. A plane geometric configuration formed by cutting a given figure with a plane which is at right angles to an axis of the figure.
- 33. The rate of change of a function occurring at or associated with a given instant, or as a limit as a time interval approaches zero; the derivative.
- 37. The rate of change of position with respect to time.
- 38. A method of obtaining the derivative of a composite function.
- 39. The rate of change of the position function occurring as a limit as a time interval approaches zero; the derivative of the position function.
- 40. The derivative of the first derivative.
- 41. The process by which an antiderivative is calculated.
- 44. The function that is integrated in an integral.
- 45. Either of the endpoints of an interval over which a definite integral is to be evaluated.
- 46. A method of approximating to an integral as the limit of a sum of areas of trapezoids.
- 48. A function that is continuous on both the left and right side at that point.
- 49. Local maximums and minimums of a function.
- 50. A rectangular sum of the area under a curve where the domain is divided into subintervals and the height of each rectangle is the function value at the right endpoint of the subinterval.
Down
- 1. The value that a function is approaching as x approaches a given value through values less than x.
- 2. The absolute value of magnitude of velocity.
- 4. Any x values where f `(x)=0 or is undefined.
- 6. The local and global maximums and minimums of a function.
- 8. The value that the function is approaching as x approaches a given value; the left and right hand limits must agree.
- 9. A point where a function changes concavity; also, where the second derivative changes signs.
- 10. The inverse operation of differentiation.
- 11. A discontinuity c of the function f for which f(c) can be redefined so that lim f(x) = f(c)
- 12. The process of finding the derivative of a function.
- 13. A function that is continuous at every point on the interval
- 14. 1/b-a{b f(x)dx
- 16. Having a decreasing derivative as the independent variable increases; having a negative second derivative.
- 18. When an absolute minimum or maximum occurs at the endpoint of the interval for which the function is defined.
- 19. [a,b]; a<x<b
- 20. (vu` - uv`)/v2
- 21. If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k.
- 23. The smallest y-value that a function achieves.
- 26. A boundary condition involving a differential equation at the beginning of the relevant time period.
- 27. Where the derivative changes signs from negative to 0 to positive.
- 28. An equation that contains derivatives or differentials of a function.
- 30. For all x in [a,b], f `(x) < 0
- 32. An integral without any specified limits, whose solution includes an undetermined constant C; antiderivative.
- 34. Derived as the ratio of the differences between the initial and final values of the two quantities constituting the ratio.
- 35. A rectangular sum of the area under a curve where the domain is divided into subintervals and the height of each rectangle is the function value at the leftmost point of the subinterval.
- 36. When testing critical values, if the first derivative changes from negative to 0 to positive, then that critical value is a local minimum of the function. If the first derivative changes from positive to 0 to negative, then that critical value is a local maximum of the function.
- 42. 1/b-a{b f(x)dx
- 43. The rate of change of the velocity with respect to time
- 47. Having an increasing derivative as the independent variable increases; a positive second derivative.