### Home > CALC > Chapter Ch3 > 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