posted by .

f(x)= x^2 / (x-2)^2
find the intervals of concavity and the inflections points

  • calc -

    I will be happy to critique your work.

  • calc -

    If the function is twice differentiable within its domain, inflection points occur at values of c where f"(c)=0.
    Note that not all points where f"(c)=0 are inflection points.

    You need to check the concavity between points where f"(x)=0. It is concave up if f"(x)>0 and concave down if f"(x)<0.

    X=c is an inflection point if all of the following conditions are satisfied:
    1. f(x) is twice differentiable at c.
    2. f"(c)=0
    3. f"(c+) has a different sign than f"(c-), i.e. concavity changes.

    Now it's time for you to sharpen your pencil and show us some work.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    y=5/x-3 find the zeros,relative min and max.the max and min find the intervals on which yis positive or negative. on which y is decreasing.intervals y concave up or down.points of inflections
  2. math-calc

    Consider the function f(x)= (2x+8)/(6x+3). For this function there are two important intervals: (-inf, A) (A, inf) and where the function is not defined at A . Find A For each of the following intervals, tell whether is increasing …
  3. calculus I

    hi! can someone please help me ... question: a)find the intervals on which f is increasing or decreasing b)find the local max and min values of f c)find the intervals of concavity and the inflection points f(x)=2x^3+3x^2-6x+1 i know …
  4. Calculus

    Consider f(x)=200+8x^3+x^4. find the intervals on which function is increasing or decreasing, the local max and minimu values, the intervals of concavity and the inflection points
  5. Calculus

    Graph the following function. Find and state the domain, intercepts, asymptotes, intervals of increase and decrease, local extrema, concavity, and inflections points. F(x)=(x+1)/(square root(x^2+1)) I got so far... Domain: (-infinity, …
  6. Calculus

    Consider the function f (x) = 2x^3 - 3x^2 - 72x + 7 Find and classify the critical points. Identify the intervals of increase and decrease, and state the intervals of concavity.
  7. calculus

    Please help!! Okay so my teacher has been away and hasent explained anything to us and we have to find the intercepts, critical points, intervals of increase and decrease, points of inflection, intervals of concavity, local maximum …
  8. Calculus

    f(x)= x/(1+x)^2 a) find the intervals on which f is increasing or decreasing. Is it ....f is decreasing on the intervals (- infinity, -1) and (1, infinity)...f is increasing on the interval (-1, 1)....... b)find the local min and max …
  9. math

    Find the intervals, inflection points and concavity for the following points. y=-2x^4+3x^2 I have the derivative: -24x^2+6
  10. MATH - CALC

    Use calculus and algebraic methods to do a complete analysis (i.e., intervals of increase and decrease, intercepts, critical points, points of inflection, and intervals of concavity) for each of the following functions and then sketch …

More Similar Questions