Home
Class 12
MATHS
Let f (x) be twice differentiable functi...

Let f (x) be twice differentiable function such that `f'' (x) lt 0` in `[0,2].` Then :

A

`f(0)+f(2)=2f(c),0ltclt2`

B

`f(0)+f(2)=2f(1)`

C

`f(0)+f(2)=f(2)gt2f(1)`

D

`f(0)+f(2)lt2f(1)`

Text Solution

Verified by Experts

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise EXAMPLE|6 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|10 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos
  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a thrice differentiable function such that |f (x) || le 1 AA x in [-1, 1], then choose the correct statement (s)

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x in R, then f^(iv)(0) is equal

Let f be a twice differentiable function such that f^(prime prime)(x)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+ (g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

Let g(x) = ln f(x) where f(x) is a twice differentiable positive function on (0, oo) such that f(x+1) = x f(x) . Then for N = 1,2,3 g''(N+1/2)- g''(1/2) =

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in (0,oo) and f(1) ne 1. Then

Let f : R ->(0,oo) and g : R -> R be twice differentiable functions such that f" and g" are continuous functions on R. suppose f^(prime)(2)=g(2)=0,f^"(2)!=0 and g'(2)!=0 , If lim_(x->2) (f(x)g(x))/(f'(x)g'(x))=1 then