Questions: The graph of the first derivative is given below. Give the intervals of increase and decrease of f.

Transcript text: The graph of the first derivative is given below Give the intervals of increase and decrease of $f$

Solution

Solution Steps

Step 1: Identify the intervals where the first derivative is positive or negative

The graph provided is of the first derivative $ f'(x) $. The function $ f(x) $ is increasing where $ f'(x) > 0 $ and decreasing where $ f'(x) < 0 $.

Step 2: Determine where the first derivative is positive

From the graph, $ f'(x) $ is positive when $ x < 0 $ and $ x > 8 $. This means $ f(x) $ is increasing on the intervals $ (-\infty, 0) $ and $ (8, \infty) $.

Step 3: Determine where the first derivative is negative

From the graph, $ f'(x) $ is negative when $ 0 < x < 8 $. This means $ f(x) $ is decreasing on the interval $ (0, 8) $.

Final Answer

The function $ f(x) $ is increasing on $ (-\infty, 0) $ and $ (8, \infty) $, and decreasing on $ (0, 8) $. Therefore, the correct option is:

Increasing on $ (-\infty, 0) $ and $ (8, \infty) $, and decreasing on $ (0, 8) $.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!