Home
Class 12
MATHS
Let f (x) be a polynomial function of de...

Let f (x) be a polynomial function of degree 3 where `a lt b lt c and f (a) =f (b) = f(c ).` If the graph of f (x) is as shown, which of the following statements are INCORRECT ? (Where `c gt|a|)`

A

`int _(a) ^(c ) f (x ) dx = int _(b) ^(c ) f (x) dx + int _(c ) ^(b) f (x) dx `

B

`int _(a) ^(c ) f (x) dx lt a`

C

` int _(a) ^(b) f (x) dx lt int _( c)^(b) f (x) dx`

D

`(1)/(b-a) int _(a ) ^(b) f(x) dx gt (1)/(c-b) int _(b) ^(c ) f (x) dx`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|6 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos

  • BIONMIAL THEOREM

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|16 Videos

Similar Questions

Explore conceptually related problems

Let f (x)= (x-a) (x-b)(x-c) be a ral vlued function where a lt b c (a,b,c in R) such that f ''(alpha ) =0. Then if alpha in ( c _(1), c _(2)), which one of the following is correct ?

If f(x) is a polynomial function of the second degree such that, f(-3)=6,f(0)=6" and "f(2)=11 , then the graph of the function, f(x) cuts the ordinate x = 1 at the point

Knowledge Check

  • The graphs shown above represent f(x) and f(x+a) + b, where a and b are constants. Which of the following is the ordered pair (a,b) ?

    A
    (1,2)
    B
    (2,1)
    C
    (-1,2)
    D
    (2,-1)

    • Similar Questions

    Explore conceptually related problems

    If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​ is equals to

    If f(x) is a polynomial of degree n(gt2) and f(x)=f(alpha-x) , (where alpha is a fixed real number ), then the degree of f'(x) is

    Let f be a real-valued function defined on interval (0,oo) ,by f(x)=lnx+int_0^xsqrt(1+sint).dt . Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo) . " " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo) , but not differentiable on (0,oo) . " " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo) . " " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo) .

    Let f(x) = (g(x))/(h(x)) , where g and h are continuous functions on the open interval (a, b). Which of the following statements is true for a lt x lt b ?

    If a lt b lt c in R and f (a + b +c - x) = f (x) for all, x then int_(a)^(b) (x(f(x) + f(x + c))dx)/(a + b) is:

    If a lt b lt c , then find the range of f(x)="|x-a|+|x-b|+|x-c|

    Let f(x) be a non - constant polynomial such that f(a)=f(b)=f(c)=2. Then the minimum number of roots of the equation f''(x)=0" in "x in (a, c) is/are

    Home
    Profile