Home > CALC > Chapter 3 > Lesson 3.3.4 > Problem 3-131
The graph of f(x) is shown at right. Use the graph to list the following values in ascending (increasing) order:
0, f ′(1), f ′(4),
3-131 HW eTool (Desmos). Homework Help ✎
f '(1) means the slope at x = 1. Is the slope at x = 1 positive, negative or zero? How does this compare with the slope at x = 4?
f '(4) means the slope at x = 4. Is the slope at x = 4 positive, negative or zero? How does it compare with the slope at x = 1?
means the average rate of change between x = 3 and x = 1.
Graphically, this can be seen as the slope of the secant line. Is that slope positive, negative or zero? How does it compare with the slopes at x = 1 and x = 4, and with the value of 0?
Looking at the graph from left to right, it is increasing always. The slopes start steep and, as x→∞, get smoother.
Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 3-131 HW eTool