Calculus

The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false? (4 points)

The graph of f has an inflection point at x = 0.

The graph of f has a relative maximum at x = 0.

The graph of f is always concave down.

The graph of the second derivative is always negative.

I know that the first two are right, but not sure about the second two.

  1. 👍
  2. 👎
  3. 👁
  1. since f' is decreasing, we know that f" < 0

    So, at x=0, the slope is 0, and the curve is concave down, so it is a max there.

    if f" is always negative, the curve is always concave down.

    Looks like they're all true.

    Consider the parabola y = -x^2

    f' = -2x, which is always decreasing, and f'(0) = 0

    f" = -2, and the parabola is always concave down.

    So, only #1 is false.

    1. 👍
    2. 👎
  2. The graph of f has an inflection point at x = 0. is the answer

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1.] f(x) = x + 7 if x < 0 2x − 5 if x ≥ 0 1 continuous discontinuous If it is not continuous on its domain, list the points of

  2. MATH

    describe how the graphes of y=/x/ and y=/x/-15 are related A:the graphs have the same shape.The y-intersept of y=/x/ is 0, and the x-intercept of the second graph is -15 B: the graphs have the same y-intercept. the second graph is

  3. Math-True OR False Please Help!

    True or False? If the inverse function of f exists, and the graph of f has a y-intercept, the y-intercept of f is an x-intercept of f^-1

  4. Mathematics

    For question 1 & 2, find the x- and y-intercept of the line. 1. -10x + 5y = 40 A. x-intercept is 5; y-intercept is -10 B. x-intercept is 8; y-intercept is -4 C. x-intercept is -10; y-intercept is 5 D. x-intercept is -4;

  1. math

    find a function y=ax^2+bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with slope -1 at the y-intercept.

  2. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

  3. Calculus

    1. The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = –3. Which of the following statements must be true? A. The graph of f is always concave down. B. The graph of f has an inflection point at x =

  4. MATH PLEASE HELP!

    True or False? If the inverse function of f exists, and the graph of f has a y-intercept, the y-intercept of f is an x-intercept of f^-1

  1. calculus

    If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true? The graph of f has an x-intercept at x = c. The graph of f has an inflection point at x = c. The graph of f has a

  2. Algebra

    A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for \$45. Let y represent the net profit (in dollars) when they have sold x tickets. Which of the

  3. Calculus

    The graph of f '(x) is continuous and decreasing with an x-intercept at x = -3. Which of the following statements must be true?

  4. algebra

    I have a problem with this: y=1.5x Questions: What is the rate of change between the variables? State whether the y values are increasing or decreasing, or neither, as x increases Give the y intercept List the coordinates of two

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