Questions: List the critical points and endpoints of the function shown here, and classify them as relative or absolute extrema. If a point is not an extrema then say so. (Order your answers so the x-coordinates are in order from least to greatest.) List the intervals on which f is increasing or decreasing, in order.

List the critical points and endpoints of the function shown here, and classify them as relative or absolute extrema. If a point is not an extrema then say so.
(Order your answers so the x-coordinates are in order from least to greatest.)

List the intervals on which f is increasing or decreasing, in order.
Transcript text: List the critical points and endpoints of the function shown here, and classify them as relative or absolute extrema. If a point is not an extrema then say so. (Order your answers so the $x$-coordinates are in order from least to greatest.) List the intervals on which $f$ is increasing or decreasing, in order.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify critical points and endpoints

The endpoints are at x = 0 and x = 5. The critical point is at x = 3.

Step 2: Classify extrema

At x = 0, f has an absolute minimum. At x = 3, f has a relative minimum. At x = 5, f has an absolute maximum.

Step 3: Identify increasing/decreasing intervals

f is increasing on the intervals [0, 1] and [3, 5]. f is decreasing on the interval [1, 3].

Final Answer:

  • Extrema:
    • Absolute minimum at (0, 0)
    • Relative minimum at (3, 0)
    • Absolute maximum at (5, 4)
  • Increasing/Decreasing Intervals:
    • Increasing: [0, 1] and [3, 5]
    • Decreasing: [1, 3]
Was this solution helpful?
failed
Unhelpful
failed
Helpful