Across
- 4. make sure or demonstrate that the equation is true or accurate
- 6. minimum the smallest value that a mathematical function can have over its entire curve
- 8. rule the function for this is d/dx(x^n) = nx^(nā1)
- 10. line a straight line that touches a function at only one point
- 11. Ļ = 3.14159265358979323846....
- 13. rule a formula for computing the derivate of the composition of two or more functions
- 14. a mathematical object that can be interpreted as an area or a generalization of area
- 15. having limits or bounds
- 20. function a function that undoes the action of another function
- 21. derivative can be used to determine the local minimum and/or maximum points of a function as well as intervals of increase and decrease
- 24. a point on a curve where a moving point on the curve must start to move backward
- 25. a function that reverses what the derivative does
- 27. rule a formula used to find the derivates of products of two or more products
- 29. a number greater than any assignable quantity or countable number (symbol ā)
- 31. function a function of the form where b is a positive real number, and in which the argument x occurs as an exponent
- 32. any point at which the value of a function is largest (a maximum) or smallest (a minimum)
- 35. rule a method of finding the derivative of a function that is the ratio of two differentiable functions.
- 36. A u-shaped curve with certain specific properties
- 38. is an ordered collection of terms in which repetition is allowed
- 39. a function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value
- 40. the sum of some set of terms of a sequence
- 42. multiple rule allows one to take constants outside a derivate and concentrate and differentiating the function of x itself
- 43. a line that continually approaches a given curve but does not meet it at any finite distance
- 45. the amount of 3-dimensional space something takes up
- 46. value theorem guarantees both a maximum and minimum value for a function under certain conditions. It states the following: If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b]
Down
- 1. a smoothly-flowing line
- 2. a number, or the result of a calculation
- 3. the derivative of the position function
- 5. limitless or endless in space, extent, or size; impossible to measure or calculate
- 7. function the inverse of exponential functions
- 9. sum is a certain kind of approximation of an integral by a finite sum
- 12. a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x.
- 16. a relationship or expression involving one or more variables
- 17. a way to test for a function is to see whether the graph of a function can be traced with a pen without lifting the pen from the paper
- 18. a mathematical diagram which shows the relationship between two or more sets of number or measurement
- 19. of change how the quantity changes over time
- 22. function a function of an angle, or of an abstract quantity
- 23. a process of finding a function that outputs the rate of change with respect to another variable
- 26. is one of the two main operations of calculus, with its inverse operation, differentiation, being the other
- 28. the branch of mathematics concerned with the rate of changes between variables (derivates) as well as areas under curves that represent functions (integrals)
- 30. value theorem if a continuous function takes on two values y1 and y2 at points a and b, it also takes on every value between y1 and y2 at some point between a and b then it is the
- 33. A line that touches a curve at a point without crossing over
- 34. how steep a line is
- 37. Mainly used for "Difference between two given values", it is used a lot in derivatives
- 41. derivative a function is the derivative of the derivative of that function
- 44. value, or values, we can put in place of a variable (such as x) that makes the equation true
- 47. value theorem 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]