there are no examples of this type of problem in my book so if you could help walk me through it - that would be extremely helpful. thanks ahead of time.

Find the extreme values of the function on the interval and where they occur.
4) F(x)=³√(x); -3</=x</=64
A. Maximum at (64, 4), and minimum at (-3, ³√-3)
B. Maximum at (-64, 4), and minimum at (0,0)
C. Maximum at (0,0), and minimum at (64,4)
D. Maximum at (64,4), and minimum at (-64,-4).

Thanks again.

  1. 👍 0
  2. 👎 0
  3. 👁 275
  1. There must be problems on extrema. The extrema occur where f' = 0. Here,

    f(x) = x^(1/3)
    f'(x) = 1/3 x^(-2/3)
    f'(x) is never zero anywhere, especially in this interval.

    So, we just want the maximum and minimum values attained on the interval. Note that f' > 0 everywhere, so it is strictly increasing. That means

    f(-3) < f(64)
    f(-3) = -∛3
    f(64) = 4
    So, those are the extrema on this interval.

    Looks like (A) to me.

    1. 👍 0
    2. 👎 0
  2. Thanks! I'll go with that and then if I do get it wrong - I'll ask for an explanation as to why from my teacher. Thanks for explaining it too :) It's starting to make more sense.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calculus

    Driving down Bald Mountain in Wyoming, Bob dean finds that he descends 1600 feet in elevation by the time he is 2.5 miles (horizontally) away from the high point on the mountain road. Find the slope of his descent (Hint: 1 mile =

    asked by Caroline on January 10, 2013
  2. Physics

    A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 32 N. The coefficient of

    asked by kelly on February 15, 2010
  3. Maths

    Alexis reads 2/5 of her book on Monday then 1/2 of the remaining pages on Tuesday then 5/9 of the remaining pages on Wednesday the nthe remaining pages on Thursday plus reads 68 more pages on Tuesday then Wednednesday how many

    asked by Isaac on April 24, 2020
  4. social studies

    Analyze the ways in which interdependence has affected both developed and developing nations. In your answer, be sure to use examples and evidence to explain the benefits and risks facing each type of nation. In your analysis,

    asked by halochick on April 17, 2018
  5. Math - Algebra 2 some1 plz help?

    in a certain math class, each student has a text book, every 2 students share a book of tables, every 3 students share a problem book, and every 4 students share a mathematics dictionary. If the total number of books is 75.. how

    asked by Agnes on December 2, 2006
  1. Physics

    After solving a difficult physics problem, an excited student throws his book straight up. It leaves his hand at 2.5 m/s from 1.5 m above the ground. A) How much time does it take until the book hits the floor? B) What's its

    asked by Kay on January 21, 2017
  2. Writing

    Excerpt - In a culture obsessed with superficial appearances, our leaders should be those who can see beyond the surface. Judging a book by its cover is the job of the consumer, bet reading the book-pondering its contents and

    asked by Arick on September 9, 2008
  3. Advanced Math

    Write an equation in standard form for a line with an x-intercept of 2 and a y-intercept of 5. I cannot find any examples of how to do this problem, all of the examples that I have show how to do it with a slope and point. Any

    asked by Lucy on June 21, 2008
  4. sociology

    Identify a movie or book, identify with examples from the movie or book three main sociological concepts (not theories) that we have studied, identify which theory (conflict, functionalist, feminist, or interactionist) was evident

    asked by Anonymous on March 29, 2011
  5. Ray Optics

    Hi, this is about thin film interference in ray optics. My book presents two similar problems, but somehow uses different paths for the same variable. I'll list out the given variables: --Problem A-- n1 < nf > n2, delta phase is

    asked by Justin on December 5, 2016

You can view more similar questions or ask a new question.