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What is the every-day use of a derivative?
To find the rate of change. Velocity, for example, is the rate of change of distance - in a specified direction. Acceleration is the rate of change of velocity.
What are 3 real life examples of rate of change?
Velocity is the rate of change of position. Acceleration is the rate of change of velocity. How fast you spend money. How fast you do a certain job done, assuming it can be split into pieces. For example, wash dishes.
How does average change help find instant rate of change in math?
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
What is a non example of a rate?
A banana is a non example of rate. They have nothing to do with each other.
What is the geometrical meaning of second derivative?
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.
