Calculus

posted by .

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<x<3 3<x<5 5<x<6
f' + - -
f" - - +

(they are both tables)

Identify the points of inflection
a. There are no points of inflection
b. (5, -1) only
c. (3,4) and (6, 3)
d. (3,4) only
e. (3,4),(6,-3), and (5, -1)

Please explain in details how you got the answer
THANK YOU :)

  • Calculus -

    Answer is b. (5,-1) only

    Explanation:
    Points of inflection are present when f"=0 or is undefined (DNE). From the first table, you can see that f" is not 0 for any values of x, but is undefined for x=5, so there can be a possible point of inflection at x=5. Then, look at the second table. Points of inflection are where concavity changes, where f" changes from one sign to another (- to +, or + to -). At x=5, the only possible point of inflection taken from the first table, f" does change from - to +, so there is a point of inflection at x=5. At x=5, f=-1, so the point is (5,-1) (aka the answer is b).

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x<(1/4) f(x) is negative, for (1/4) <x<1 f(x) is positive, f(1/4)=0, f (2/3)=1, f ' (1/3)= …
  2. calculus

    f(x) = ln x, [1, 6] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
  3. math

    let fbe a function that is even and continuous on the closed interval [0,3]. the function f and itsderivatives have the properties indicated in the table below. sketch the graph. x 0 0<x<1 1 1<x<2 2 2<x<3 f(x) 1 (+) …
  4. Calculus

    Let f be a continuous function on the interval [0,2] which satisfies integral of f(x)dx=5 when b is 2 and a is 0. Give this information compute the definite integral f(2y)dy when b is 1 and a is 0. Solve this
  5. Math11

    Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
  6. Calculus URGENT

    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = √x [0, 9] c=?
  7. Calculus 1

    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sqrt(x), [0,16]
  8. Calculus

    Consider the function f(x) = {0, x = 0 and 1 - x, 0 <= x <= 1}. Which of the following statements is false?
  9. Calculus

    If f is differentiable at x=c, which of the following statements must be true?
  10. Continuity Calculus Help

    The given function is defined for all x > 0 except at x = 8. Find the value that should be assigned to f(8), if any, to guarantee that f will be continuous at 8. (If an answer does not exist, enter DNE.) f(x)= Sqrt( x^2-64/x-8)

More Similar Questions