Across
- 3. The value of the derivative at a particular moment. Change in the derivative value at a specific point.
- 6. f'(g(x))g'(x). Formula used to find the derivative of a composit function.
- 7. The highest point of a function. A point where the function obtains its greatest possible value.
- 9. gf'+fg'. Used when differentiating problems where one function is multiplied by another function.
- 13. The slope of the line tangent to a function. Rate of change of the corresponding function at the given point.
- 14. A ____ of a function y=f(x) is a point (c,f(c)) on the graph of f(x) at which either the derivative is 0 or the derivative is not defined. The graph of a function has either a horizontal tangent or a vertical tangent at this.
- 16. The value that a function approaches as x approaches a given value through values more than x. The value of the function that approaches when the variable approaches its limit from the right.
- 19. The lowest point of a function. A point where the function obtains its least possible value.
- 20. Used to examine where a function is increasing or decreasing on its domain. Also used to identify its local maxima and minima.
Down
- 1. When a function has a well-defined derivative for each element of the domain. A function f is _______ at a if f'(a) exists.
- 2. A sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the right endpoint of the sub-interval. A ________ uses rectangles whose top-right vertices are on the curve.
- 4. The distance between a number and the origin. Always positive.
- 5. A function with a graph that moves downward from left to right. When the y-value decreases as the x-value increases.
- 8. The value that a function approaches as x approaches a given value through values less than x. The value of the function that approaches when the variable approaches its limit from the left.
- 10. A function that moves upward from left to right. When the y-value increases as the x-value increases.
- 11. Determines whether the function is concave up, down, or neither at a point. Systematic method of finding the maximum and minimum value of a closed value function defined on a closed or bounded interval.
- 12. The value that a function approaches as the domain variable approaches a specific value. A value that a function approaches the output for the given input values.
- 15. Finding the derivative of the numerator and denominator to evaluate the limit of a function. This helps us calculate a limit that may otherwise be hard or impossible.
- 17. A line that touches a curve at a point without crossing the curve. A straight line that just barely touches a curve at one point.
- 18. A function obtained by switching the x and y variables in a function. A function that undoes the operation of f.