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3-131.

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