Question

List the coordinates of 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. y 2 X 2 (Order your answers so the x-coordinates are in order from least to greatest.) f has a relative minimum that is also an absolute minimum at $(x, y) = ( )$. f has a relative maximum that is also an absolute maximum at $(x, y) = ( )$. f has a relative maximum at $(x, y) = ( )$. f has a relative minimum at $(x, y) = ( )$. List the intervals on which $f$ is increasing or decreasing, in order. f is increasing on the interval $[ , ]$. f is decreasing on the interval $[ , ]$. f is decreasing on the interval $[ , ]$. Viewing Saved Work Revert to Last Response Submit Answer

          List the coordinates of 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.
y
2
X
2
(Order your answers so the x-coordinates are in order from least to greatest.)
f has a relative minimum that is also an absolute minimum at $(x, y) = (		)$.
f has a relative maximum that is also an absolute maximum at $(x, y) = (		)$.
f has a relative maximum at $(x, y) = (		)$.
f has a relative minimum at $(x, y) = (		)$.
List the intervals on which $f$ is increasing or decreasing, in order.
f is increasing on the interval $[		,		]$.
f is decreasing on the interval $[		,		]$.
f is decreasing on the interval $[		,		]$.
Viewing Saved Work Revert to Last Response
Submit Answer

Show more…

List the coordinates of 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.
y
2
X
2
(Order your answers so the x-coordinates are in order from least to greatest.)
f has a relative minimum that is also an absolute minimum at (x, y) = ( ).
f has a relative maximum that is also an absolute maximum at (x, y) = ( ).
f has a relative maximum at (x, y) = ( ).
f has a relative minimum at (x, y) = ( ).
List the intervals on which f is increasing or decreasing, in order.
f is increasing on the interval [ , ].
f is decreasing on the interval [ , ].
f is decreasing on the interval [ , ].
Viewing Saved Work Revert to Last Response
Submit Answer

Added by Douglas S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

10/31/2022

Step 1

To find the critical points, we need to find the values of x where the derivative of the function is equal to zero or undefined. Show more…

Show all steps

lock

Thanks for your feedback!

List the coordinates of 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.) f has a relative minimum that is also an absolute minimum vv at (x,y)= f has a relative maximum that is also an absolute maximum vv at (x,y)=(,). f has a relative maximum ,vv at (x,y)=(^(◻)). f has , ] at (x,y)=(,). List the intervals on which f is increasing or decreasing, in order. f is increasing V on the interval f is decreasing ✓ on the interval f is decreasing ✓ on the interval Viewing Saved Work Revert to Last Response List the coordinates of 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. y (Order your answers so the x-coordinates are in order from least to greatest. f has a relative maximum that is also an absolute maximum ] at (x, y) = ( f hasa relative maximum v] at (x, y) =( v at (x, y) = ( f hasa relative minimum List the intervals on which f is increasing or decreasing, in order. f is[increasing v]on the interval f is[decreasing v] on the interval f is[decreasing v]on the interval Viewing Saved Work Revert to Last Response Submit Answer

Play audio

Feedback

Powered by NumerAI

Andrew Noble and 71 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Here, we're given a function f of x, which is equal to 5x squared minus 20x plus 5.

00:06 And we want to find the locations of any maximums and minimums, as well as where it's increasing and decreasing.

00:12 To do that, we need to first start off with the critical points, because the critical points are places where it can change direction.

00:18 So, let's take the derivative and set that equal to zero, because that's where the critical points will be.

00:23 So the derivative of 5x squared, that's a power rule.

00:26 We just get 5 times 2 is 10, x, minus 20x gives us, 20 and add 5, well, that's a constant, so it goes away.

00:34 So when we set that equal to zero, i'm just going to add 20 and divide by 10 to get that x is equal to 20 over 10 or 2.

00:41 So in this case, there's only one critical point.

00:44 We could have as many critical points as we want.

00:48 You'll also notice that we were talking about the domain from zero to three.

00:55 So now let's go ahead and find out which one of these is a maximum or a minimum.

01:02 We can do that by just saying what is f of each of these points.

01:06 So 2, 0, 3.

01:12 If i plug in 0, i'm going to get 5.

01:15 If i plug in 2, i'm going to get 5 times 4 is 20 minus 2 times 20.

01:20 So that's going to be negative 20 plus 5 is negative 15.

01:24 If i plug in 3, i'm going to get 5 times 9 is 45 minus 60.

01:29 So that's going to be negative 15 plus 5 is negative 10...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later