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The graph shows the derivative,
f(x), for a piecewise function
f(x).
a. Determine the intervals of
x where
f(x) is increasing, decreasing, and constant. Justify your answers!
(Have to use the graph of the derivative given - to make conclusions about the graph of the original/actual function!)
Increasing:
Decreasing:

The graph shows the derivative, $f(x)$ , for a piecewise function $f(x)$ . $\newline$ a. Determine the intervals of $x$ where $f(x)$ is increasing, decreasing, and constant. Justify your answers! $\newline$ (Have to use the graph of the derivative given - to make conclusions about the graph of the original/actual function!) $\newline$ Increasing: $\newline$ Decreasing:

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Identify independent and dependent variables

Full solution

Q. The graph shows the derivative,

f(x)

, for a piecewise function

f(x)

.

\newline

a. Determine the intervals of

x

where

f(x)

is increasing, decreasing, and constant. Justify your answers!

\newline

(Have to use the graph of the derivative given - to make conclusions about the graph of the original/actual function!)

\newline

Increasing:

\newline

Decreasing:

Find Increasing Intervals: To find where $f(x)$ is increasing, look for where its derivative, $f'(x)$ , is positive on the graph.
Find Decreasing Intervals: For decreasing intervals, find where $f'(x)$ is negative.
Identify Constant Intervals: Where $f'(x)$ is zero, $f(x)$ is constant.
Graph Analysis: Increasing: If the graph of $f'(x)$ is above the x-axis, then $f(x)$ is increasing. Let's say $f'(x) > 0$ from $x = 1$ to $x = 3$ .

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