Home
Class 12
MATHS
The graph of the second derivation f''(x...


The graph of the second derivation f''(x) is given in the following figure. State the x - coordinate of the point of inflection of f. Given reasons for your answer.

Text Solution

Verified by Experts

x = 1 is the point of inflection as f'' changes sign from '-' to '+' with f''(1) = 0.
So the concavity of the curve changes from downward to upward.
x = 7 is the point of inflection as f'' changes sign from '+' to '-' with f''(7) = 0. So the concavity of curve changes from upward to downward.
At x = 4, f'' = 0, but f'' does not change sign. So x = 4 is not a point of inflection.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.25|1 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.26|1 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.23|1 Videos

  • FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|7 Videos

  • GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|18 Videos

Similar Questions

Explore conceptually related problems

The graph of the derivative f'(x) is given in the following figure. (b) Find the values of x for which f has local maximum or minimum. (c) Find the intervals in which f is concave upward or downward. (d) Find the point of inflection.

The graph of y = f(x) is as shown in the following figure. Identify the points of discontinuity and give the reason for the same.

Knowledge Check

  • Find the points of inflection for f(x)=3x^(4)-4x^(3) .

    A
    0
    B
    1
    C
    `2/3`
    D
    `-2`

    • Similar Questions

    Explore conceptually related problems

    The graph of y=f(x) is as shown in the following figure. Draw the graph of y=[f(x)] .

    Graph of y=f(x) and y=g(x) is given in the following figure. If h(x)= f(g(x)) , then find the value of h'(2) .

    In which of the following graphs is x=c the point of inflection? figure (b) figure (c) figure (d) figure

    Find the derivative of f(x) = 10x.

    Graph of y = f(x) is as shown in the following figure. Find the roots of the following equations f(x) = 0 f(x) = 4 f(x) = x + 2

    Find the derivative of f(x) = x^(2) .

    Draw the graph of f(x)="ln" (1-"ln "x) . Find the point of inflection.

    Home
    Profile