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"Rate of change" means how quickly something changes. Examples in physics include a speed as a rate of change of position - if your position changes 10 meters every second, then that (10 meters/second) is your rate of change of position, or your velocity. Or if your income increases by a thousand dollars a year, then that's the rate of change of your income - how quickly your income changes.
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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.
How is the steepness of the line is related to the rate of change?
the steepness of the line is the slope of the line which is the rate of change; the steeper the slope, the faster the rate of change
Why do take derivative?
To find rate of change. Two common examples are: rate of change in position = velocity and rate of change of velocity = acceleration.
What is the rate of change in position called?
Rate of change in position is called velocity.
What does a shallow slope on a graph say about the rate of change?
A low rate of change.
