if f(x) be a twice differentiable funct...

if f(x) be a twice differentiable function such that `f(x) =x^(2) " for " x=1,2,3,` then

`f''(x) = 2 AA x in (1, 3)`

f''(x) = 2 for some `x in (1,3)`

`f''(x) = 3 AA x in (2,3)`

f''(x) = f'(x) for some `x in (2,3)

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
MCGROW HILL PUBLICATION|Exercise Exercise ( NUMERICAL ANSWER TYPE QUESTIONS)|17 Videos
APPLICATIONS OF DERIVATIVES
MCGROW HILL PUBLICATION|Exercise Question for Previous Year.s AIEEE/JEE Main Paper|65 Videos
APPLICATIONS OF DERIVATIVES
MCGROW HILL PUBLICATION|Exercise Exercise ( LEVEL-1 SINGLE CORRECT ANSWER TYPE QUESTIONS)|45 Videos
AREA BY INTEGRATION
MCGROW HILL PUBLICATION|Exercise Question from Previous Years. B-Architecture Entrance Examination Papers|12 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

If f(x) is a twice differentiable function and given that f(1)=2,f(2)=5 and f(3)=10 then

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

If f:R to R is a twice differentiable function such that f''(x) gt 0" for all "x in R, and f(1/2)=1/2, f(1)=1 then :

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

If f(x) is a twice differentiable function such that f(a)=0,f(b)=2,f(c)=-1,f(d)=2,f(e)=0 where a

Let f(x) be twice differentiable function such that f'(0) =2 , then, lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2) , is

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

MCGROW HILL PUBLICATION-APPLICATIONS OF DERIVATIVES-Exercise ( LEVEL-2 SINGLE CORRECT ANSWER TYPE QUESTIONS)

The smallest value of M such that |x^2-3x+2| leq M for all x in [1,5/2...
Text Solution
|
The point in the interval [0, pi] for which the curve y =(1//2)x and y...
Text Solution
|
The points at which the tangents to the curve ax^(2) + 2hxy + by^(2) =...
Text Solution
|
If the point on y = xtanalpha -(ax^2)/(32cos^2alpha),(alpha > 0) where...
Text Solution
|
Let f(x) = {(|x-1|+ a",",x le 1),(2x + 3",",x gt 1):} . If f(x) has lo...
Text Solution
|
Let g(x) = int(0)^(x) f(t) dt and f(x) satisfies the equation f(x +y) ...
Text Solution
|
The area of the triangle formed by the positive x-axis with the norma...
Text Solution
|
The interval in which the function y = f(x) = (x-1)/(x^2-3x+3) transfo...
Text Solution
|
Angle at which the circle x^2+y^2=16 can be seen from (8, 0) is
Text Solution
|
The critical points of the function f(x) = (x +2)^(2//3) (2x-1) are
Text Solution
|
The function f(x)=(log(pi+x))/(log(e+x))s is
Text Solution
|
A rectangle with perimeter 32 cm has greatest area if its length is
Text Solution
|
The greatest vaue of the function f(x) = cot^(-1) x + (1//2) log x ...
Text Solution
|
A particle is moving along the parabola y^(2) = 4(x+2). As it passes t...
Text Solution
|
The perimeter of a rectangle is fixed at 24cm. If the length l of the ...
Text Solution
|
The rate at which fluid level inside vertical cylindrical tank of radi...
Text Solution
|
The length x of a rectangle is increasing at the rate of 3 cm/sec. and...
Text Solution
|
if f(x) be a twice differentiable function such that f(x) =x^(2) " fo...
Text Solution
|
A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-ax...
Text Solution
|
If f(x) = x^(3) + bx^(2) + cx +d and 0lt b^(2) lt c.then in (-infty, i...
Text Solution
|