CPM Homework Help : APCALC Problem 3-131

The graph of $y = f(x)$ is shown at right. Use the graph to list the following values in ascending (increasing) order:

$0, f^\prime(1), f ^\prime(4),\frac { f ( 3 ) - f ( 1 ) } { 3 - 1 }$

Hint:

$f ^\prime(1)$ means the slope at . Is the slope at $x = 1$ positive, negative or zero? How does this compare with the slope at $x = 4$ ?

Hint:

$f ^\prime\left(4\right)$ means the slope at $x = 4$ . Is the slope at $x = 4$ positive, negative or zero? How does it compare with the slope at $x = 1$ ?

Hint:

$\frac{f(3)-f(1)}{3-1}$

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 $0$ ?

Hint:

Looking at the graph from left to right, it is increasing always. The slopes start steep and, as $x \rightarrow \infty$ , get smoother.

First quadrant, increasing curve, opening down, starting at the origin, passing through the approximate points, (1, comma 2), (3, comma 3), (4, comma 3.5), continuing up & right.

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