at
the point x
= 1.4.3 Equations of Tangents
The derivative tells us what the rate of change a curve is undergoing at any particular instant.
A positive value tells us that the function is increasing at the point.
A negative value tells us that the function is decreasing at the point.
A value of zero tells us that the function is neither increasing nor decreasing. This implies a maximum or minimum value.
Ex 1
Find the equation of the tangent to the curve
at
the point x
= 1.
What do we need to define a line? What is the most efficient way to find all the information?
Ex 2
Find the coordinates on the curve
where
the tangent is horizontal.
Options: graph on GDC and calculate max and min points.
calculate the derivative and set it equal to zero.
p. 618#1-5