Calculus

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x).

I found the first and second derivative which i think is (8x+1)/(x^(2/3), and the second is 2(4x-1)/3x^(5/3). what now?

  1. 👍 0
  2. 👎 0
  3. 👁 299
asked by Tom
  1. Assuming x is not zero, the fractions are zero when the numerators are zero.

    So,

    f'=0 when 8x+1 = 0, or x = -1/8
    f"=0 when 4x-1 = 0, or x = 1/4

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus AB

    Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f '(x) and f "(x). My start to a solution: x-values: (-1/8) and

    asked by Vikram on January 11, 2016
  2. Math Calc

    Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f '(x) and f "(x) I got -1/8 for a minimum point and 1/4 for

    asked by Ke$ha on January 5, 2017
  3. Calculus

    Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)=9x^1/3+9/2x^4/3. I've gotten -0.5 as the relative minimum and x=1 for the inflection points. Is this correct? If not, can you show me how

    asked by Kait on December 17, 2017
  4. Calculus

    Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). Please use an analysis of f ′(x) and f ′′(x).

    asked by Mel on January 8, 2016
  5. calculus

    Find all relative extrema and points of inflection of the function: f(x) = sin (x/2) 0 =< x =< 4pi =< is supposed to be less than or equal to. I can find the extrema, but the points of inflection has me stumped. The inflection

    asked by James on November 14, 2010
  6. Calculus

    Find the intercept, relative extrema, point of inflection, and asymptotes of the function(if they exist)of: y= 3[(x-1)^(2/3)] - [(x-1)^2]

    asked by Jands on January 10, 2011
  7. Calculus

    Find the intercept, relative extrema, point of inflection, and asymptotes of the function(if they exist)of: y = (x^2 + 1)/(x^2 - 9)

    asked by Jands on January 10, 2011
  8. Calculus

    Find the intercept, relative extrema, point of inflection, and asymptotes of the function(if they exist)of: y = (x^3)/(x^2 - 4)

    asked by Jands on January 10, 2011
  9. Calculus

    Find the intercept, relative extrema, point of inflection, and asymptotes of the function(if they exist)of: y= (x^4) - 8(x^3) + 18(x^2) - 16x + 5

    asked by Jands on January 10, 2011
  10. calculus

    find the relative extrema and points of inflection, if possible, of y = xln((x^4)/8) Any help would be awesome...thanks! (i know that the relative extrema come from critical values from y' and points of inflection come from y'')

    asked by Juliet on January 19, 2012

More Similar Questions