Activity 3

2. the location of a particle along the x and y axis. Its derivative finds the velocity.
3. A point in the graph of a function where the function does not exist. The limit does exist at that point.
5. the name of theorem which requires continuity and differentiabilty over the interval. If conditions are met, there must be an x such that f'(x) equals the average value.
6. a method to differentiate a function divided by a function. the denominator becomes the denominator squared.
8. This is a way to imagine the area under a curve. One way to think of it is the limit of the difference between the value of the function at x and the value of the function at x plus a value, all divided by that increase.
11. points where the first derivative is equal to zero or does not exist. The tangent to the function is horizontal.
14. a method to differentiate a function divided by a function. the derivatives are multiplied by the originals.
15. its derivative is 1/x. Answers what value e must be raised to to get x.
17. the way to take the derivative of a polynomial. Multiply the exponent of the polynomial by the original function but decrease the exponent by one.
18. the speed of a particle at a certain point. If it is positive, the position is increasing.
19. This is the instantaneous rate of change. It finds the changing slope of a curve.
20. a method to evaluate limits that come to indeterminate form with substitution. This rule comes from a French scientist.

1. the points of a function where it changes from increasing to decreasing. They can be identified using critical numbers.
4. This is the way to take the derivative of a function inside a function. Multiply the derivative of the inside function by the derivative of the inside function, keeping the inside function consistent.
7. the rate of increase or decrease of a curve. It is not consistent unless in a linear function.
9. This the the value that a function approaches as x approaches a value. The value of this and the value of the function at a certain x do not have to be equivalent.
10. A point in the graph where one would have to pick up their pen to continue drawing it. This means that there are points for which the limit does not exist.
12. the rate at which the velocity changes. If it has the same sign as velocity, the velocity is increasing.
13. this theorem is a special case of the mean value theorem. The values of the endpoints are equivalent.
16. Functions that undo each other. The notation is f^-1.