Calculus

26. Find all points of inflection.

f(x) = (5x-3)^(1/3)

Note: I have gotten
f''(x) = (-50/9)(5x-3)^(-5/3)
I would like to know how to figure out the zeros.

  1. 👍
  2. 👎
  3. 👁
  1. you want to have (-50/9)(5x-3)^(-5/3) = 0
    then (5x-3)^(-5/3) = 0
    or
    1/(5x-3)^(5/3) = 0

    Clearly this has no solution.
    Think of it this way:
    1 divided by what number would give you zero?? There is no such number

    So since your equation has no solution, there is no point of inflection.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any

  2. Calculus

    Suppose f is continuous on [0, 6] and satisfies the following x 0 3 5 6 f -1 4 -1 -3 f' 5 0 -8 0 f" -1 -3 DNE 3 x 0

  3. calculus

    3. Given the function defined by y = x + sinx for all x such that -π/2

  4. calculus

    Find any relative extrema and any points of inflection if they exist of f(x)=x^2+ ln x^2 showing calculus. Please show work in detail so I can follow. Thanks. The answer is no relative max or min and the points of inflection are

  1. Calculus

    1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

  2. 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

  3. Calculus

    If f(x) is a continuous function with f"(x)=-5x^2(2x-1)^2(3x+1)^3 , find the set of values for x for which f(x) has an inflection point. A. {0,-1/3,1/2} B. {-1/3,1/2} C. {-1/3} D. {1/2} E. No inflection points

  4. 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

  1. APCalculus

    For the function y=2sin(x)-cos^2(x) on [0, 2pi] find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points

  2. Calculus

    Here is a graph of the derivative y’ of a continuous, differentiable function. For approximately what values of x between -5 and 5 does the original function y have inflection points. Is it 4 inflection points?

  3. calculus

    Let f (x) = x^2 + 5x-14. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The

  4. geometry CA

    Graph quadrilateral ABCD. Then determine the most precise name for each quadrilateral. 1. A (0, 5), B (–5, 0), C (0, –5), D (5, 0) (1 point) square kite rectangle 2. A (–4, 4), B (3, 4), C (5, 0), D (–2, 0) (1 point)

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