Across
- 3. - The Mean Value Theorem 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].
- 5. - method for differentiating problems where one function is divided by another.
- 6. - If f' (x) changes from negative to positive at c, then f(c) is a relative minimum.
- 9. - a value that a function approaches as an input of that function gets closer and closer to some specific number
- 13. - involve two (or more) variables that change at the same time, possibly at different rates
- 14. - the rate of change of a function with respect to a variable.
- 16. - allows you to find the derivative of y with respect to x without having to solve the given equation for y.
- 20. - to calculate the area under a continuous graph and the tangent line at every point on the graph.
- 25. - a point within an interval at which the function has a minimum value.
- 28. - a place where the function is undefined and the limit of the function does not exist.
- 29. - a point within an interval at which the function has a maximum value
- 31. - an approximation of a region's area, obtained by adding up the areas of multiple simplified slices of the region.
- 33. - a point on the graph of a function at which the concavity changes.
- 34. - a function built from pieces of different functions over different intervals.
- 35. - a function whose graph is continuous without any breaks or jumps
Down
- 1. - the lowest value across a whole domain of a function:
- 2. - the rate of change of the rate of change
- 4. - a point at which the derivative is zero or undefined.
- 7. - a point at which a maximum or minimum value of the function is obtained in some interval.
- 8. - if a function f(x) is continuous over an interval [a, b], then the function takes on every value between f(a) and f(b).
- 10. - the rate of change of a function's derivative.
- 11. - a function that is continuous over a closed interval is guaranteed to have a maximum or minimum value over a closed interval.
- 12. - the change in the rate at a particular instant, and it is same as the change in the derivative value at a specific point.
- 15. - an equation that relates one or more unknown functions and their derivatives.
- 17. - first function multiplied by the derivative of the second, and the second function multiplied by the derivative of the first function.
- 18. - a differentiable function F whose derivative is equal to the original function f.
- 19. - the difference of the values at points a and b.
- 21. - It is a measure of how much the function changed per unit over an interval.
- 22. - anything that is similar, but not exactly equal, to something else.
- 23. - looking for the largest value or the smallest value that a function can take.
- 24. - a function whose derivative exists at each point in its domain.
- 26. - the line of the slope of the curve at a particular point.
- 27. - f(g(x)) is f'(g(x))⋅g'(x).
- 30. - the rate of change of velocity
- 32. - the derivative of the position function.