45 - 46. analyzing slopes use the points a, b, c, d, and e in the following graphs to answer these…

Explanation:

Step1: Recall slope - sign rules

The slope of a curve at a point is the slope of the tangent line at that point. If the curve is increasing at a point, the slope of the tangent is positive. If the curve is decreasing at a point, the slope of the tangent is negative.

Step2: Find points with negative slope

The curve is decreasing at points $C$ and $E$. So the points with negative slope are $C$ and $E$.

Step3: Find points with positive slope

The curve is increasing at points $A$ and $D$. So the points with positive slope are $A$ and $D$.

Step4: Analyze steepness for slope order

The steepness of the curve at a point is related to the magnitude of the slope. The steeper the curve, the larger the magnitude of the slope. At point $A$, the curve is quite steep and increasing. At point $D$, the curve is less steep and increasing. At point $C$, the curve is less steep and decreasing. At point $E$, the curve is steeper and decreasing. The slope at $B$ is 0 (since it is a local maximum). The slopes in decreasing order are $A$, $D$, $B$, $C$, $E$.

Answer:

a. $C$, $E$ b. $A$, $D$ c. $A$, $D$, $B$, $C$, $E$