"The derivative of at "
"The slope of at "
Find the slope of at
Apply the definition of slope
Thus, the slope at is
Rate of Change
The physical interpretation of derivatives is that they measure rates of change.
If the distance to an object at time is then its:
SPEED Speed ignores direction
An object dropped near Earth travels meters in seconds. How far do you need to drop an object so that it hits the ground at ?
Find speed at time
Find the distance traveled at
Thus, we must drop the object from a height of 4.9m.
Gregor Mendel discovered the laws of ''genetic inheritance'' by studying populations of peas.
He found: If is the percentage of smooth skinned peas in a population then the proportion in the next generation will be:
When does change most as a function of ?
Thus, the proportion changes most when
That is, introducing a few smooth skin peas will have the largest affect on the population
We need a more systematic way of calculating derivatives.
If for all then
Why is this true?
If for some number then
Why is this true ? Transformation