Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

ermine relative extrema algcbraically. udent/PlayerTest. aspxquizme =18 chapterld =88 sectionild =28 bjectiveld =48 studyPlanAssignmentid =24379978 viewMode =08c... William Artiaga 04/18/24 12:35 AM -2-4 Determine This quiz: 5 point(s) possible ebraically. Question 3 of 5 This question: 1 point(S) possible Resume later Submit quiz Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x)=5+(4+3x)^(2//3) A. There are no relative minima. The function has a relative maximum of ◻ at x= ◻ T. (Use a comma to separate answers as needed.) B. There are no relative maxima. The function has a relative minimum of ◻ at x= ◻ . (Use a comma to separate answers as needed.) c. The function has a relative maximum of ◻ at x= ◻ and a relative minimum of ◻ att x= ◻ . (Use a comma to separate answers as needed.) D. There are no relative extrema. Next esk 1

ermine relative extrema algcbraically.\newlineudent/PlayerTest. aspxquizme =18 =18 chapterld =88 =88 sectionild =28 =28 bjectiveld =48 =48 studyPlanAssignmentid =24379978 =24379978 viewMode =08c =08 \mathrm{c} ...\newlineWilliam Artiaga 0404/1818/2424 1212:3535 AM\newline−2-2−4-4 Determine\newlineThis quiz: 55 point(s)\newlinepossible ebraically.\newlineQuestion 33 of 55\newlineThis question: 11\newlinepoint(S) possible\newlineResume later\newlineSubmit quiz\newlineFind the x x -values of all points where the function has any relative extrema. Find the value(s) of any relative extrema.\newlinef(x)=5+(4+3x)2/3 f(x)=5+(4+3 x)^{2 / 3} \newlineA. There are no relative minima. The function has a relative maximum of □ \square at x= x= □ \square T.\newline(Use a comma to separate answers as needed.)\newlineB. There are no relative maxima. The function has a relative minimum of □ \square at =88 =88 11 □ \square .\newline(Use a comma to separate answers as needed.)\newlinec. The function has a relative maximum of □ \square at x= x= □ \square and a relative minimum of □ \square att x= x= □ \square .\newline(Use a comma to separate answers as needed.)\newlineD. There are no relative extrema.\newlineNext\newlineesk 11

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Reflections of functionsright chevron icon

Full solution

Q. ermine relative extrema algcbraically.\newlineudent/PlayerTest. aspxquizme =18 =18 chapterld =88 =88 sectionild =28 =28 bjectiveld =48 =48 studyPlanAssignmentid =24379978 =24379978 viewMode =08c =08 \mathrm{c} ...\newlineWilliam Artiaga 0404/1818/2424 1212:3535 AM\newline−2-2−4-4 Determine\newlineThis quiz: 55 point(s)\newlinepossible ebraically.\newlineQuestion 33 of 55\newlineThis question: 11\newlinepoint(S) possible\newlineResume later\newlineSubmit quiz\newlineFind the x x -values of all points where the function has any relative extrema. Find the value(s) of any relative extrema.\newlinef(x)=5+(4+3x)2/3 f(x)=5+(4+3 x)^{2 / 3} \newlineA. There are no relative minima. The function has a relative maximum of □ \square at x= x= □ \square T.\newline(Use a comma to separate answers as needed.)\newlineB. There are no relative maxima. The function has a relative minimum of □ \square at =88 =88 11 □ \square .\newline(Use a comma to separate answers as needed.)\newlinec. The function has a relative maximum of □ \square at x= x= □ \square and a relative minimum of □ \square att x= x= □ \square .\newline(Use a comma to separate answers as needed.)\newlineD. There are no relative extrema.\newlineNext\newlineesk 11
  1. Find Critical Points: To find relative extrema, we need to find the first derivative of f(x)f(x) and set it equal to 00 to find critical points.
  2. Differentiate with Chain Rule: Differentiate f(x)f(x) with respect to xx using the chain rule: f′(x)=(23)(4+3x)−13⋅3f'(x) = \left(\frac{2}{3}\right)\left(4+3x\right)^{-\frac{1}{3}} \cdot 3.
  3. Simplify the Derivative: Simplify the derivative: f′(x)=23×3×(4+3x)−13=2×(4+3x)−13f'(x) = \frac{2}{3} \times 3 \times (4+3x)^{-\frac{1}{3}} = 2 \times (4+3x)^{-\frac{1}{3}}.
  4. Set Derivative Equal to Zero: Set the derivative equal to zero to find critical points: 2×(4+3x)−13=02 \times (4+3x)^{-\frac{1}{3}} = 0.
  5. No Critical Points or Extrema: Since the term 4+3x)−1/3 cannotbezero,therearenorealvaluesof$x4+3x)^{-1/3}\ cannot be zero, there are no real values of \$x that will make f′(x)f'(x) equal to zero. Therefore, there are no critical points and no relative extrema.
  6. Final Answer: The correct answer is D. There are no relative extrema.

More problems from Reflections of functions

Question
Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=9∣x+2∣−4f(x)=9|x+2|-4.\newlineChoices:\newline(A)g(x)=9∣x+2∣−4]\text{}(A)g(x) = 9|x+2| - 4\text{]}\newline(B)g(x)=9∣x−2∣−4]\text{}(B)g(x) = 9|x-2| - 4\text{]}\newline(C)g(x)=−9∣x−2∣+4]\text{}(C)g(x)=-9|x-2| +4\text{]}\newline(D)g(x)=−9∣x+2∣+4]\text{(D)}g(x) = -9|x + 2| + 4\text{]}
Get tutor helpright-arrow

Posted 2 months ago

Question
What does the transformation f(x)↦f(x−4) f(x) \mapsto f(x - 4) do to the graph of f(x) f(x) ?\newlineChoices:\newline(A) translates it 4 units right\text{translates it } 4 \text{ units right}\newline(B) translates it 4 units down\text{translates it } 4 \text{ units down}\newline(C) translates it 4 units left\text{translates it } 4 \text{ units left}\newline(D) translates it 4 units up\text{translates it } 4 \text{ units up}
Get tutor helpright-arrow

Posted 2 months ago

Question
What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically
Get tutor helpright-arrow

Posted 1 month ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 99 units down of f(x)=10x+8f(x) = 10x + 8.\newlineChoices:\newline(A) g(x)=10x−82g(x) = 10x - 82 \newline(B) g(x)=10x+98g(x) = 10x + 98 \newline(C) g(x)=10x−1g(x) = 10x - 1\newline(D) g(x)=10x+17g(x) = 10x + 17
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}
Get tutor helpright-arrow

Posted 1 month ago

Question
The parabola y=x2y=x^{2} is scaled vertically by a factor of 77. What is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 4 months ago

Question
The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 4 months ago

Question
The parabola y=x2y=x^{2} is shifted up by 22 units and to the right by 33 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 1 month ago

Question
The parabola y=x2 y=x^{2} is reflected across the x x -axis and then scaled vertically by a factor of 55 .\newlineWhat is the equation of the new parabola?\newliney=□ y=\square
Get tutor helpright-arrow

Posted 2 months ago

Question
The parabola y=x2 y=x^{2} is scaled vertically by a factor of 110 \frac{1}{10} .\newlineWhat is the equation of the new parabola?\newliney= y=
Get tutor helpright-arrow

Posted 3 months ago

View all (24)