Calculus Crossword

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^(n−1)
10. line a straight line that touches a function at only one point
11. π = 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 ∞)
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]