Find all slopes of the curve at the given point. [It may be helpful to graph the curve.]
B) -3 and 0
C) -3 and 3
D) 0, undefined

Question

Find all slopes of the curve at the given point. [It may be helpful to graph the curve.] 
B) -3 and 0 
C) -3 and 3 
D) 0, undefined

Quizplus · Accepted Answer

From the graph, it is clear that the slope is negative at the point where x=0, indicating that the curve is decreasing at that point. This rules out choices A, B, and D. At the point where x=3, the slope is zero as the curve is flat. However, at the point where x=-3, the slope is positive, indicating that the curve is increasing at that point. Therefore, the solution is C, which lists both the slopes (-3 and 3) that the curve has at the given points.

Find All Slopes of the Curve at the Given Point