4.1 Increasing and Decreasing Functions
We say that a function is increasing on an interval if for any value of
.
We
Increasing Function
How does the derivative
on the interval,
Decreasing function
relate to whether or not a function is increasing?
Where can a function change from decreasing y values to increasing ones, or vice versa?
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Do the above features guarantee a change from increasing values to decreasing ones, or vice
versa?
Ex 1: Where is the function
increasing?
Ex 2: What are the intervals of increasing and decreasing for the function
Ex 3: Sketch the graph of a function, f(x), that is differentiable and satisfies the following
conditions:
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Ex 4: For the function given by
, determine the values of b,c, and d
such that f(x) decreases to the point (0,2), increases to the point (2,10) and then continues to
decrease.
Ex 5: The following function represents the derivative function f’(x) of a function f(x).
Determine the intervals of increase and decrease f(x) and the x-coordinate of the local
extrema (max/min) of f(x). Also sketch f(x).