Home
Class 12
MATHS
If f:[0,1] to [0,prop) is differentiable...

If `f:[0,1] to [0,prop)` is differentiable function with decreasing first derivative suc that f(0)=0 and `f'(x) gt 0`, then

A

`f(1)gef'(1)`

B

`f'(c)ne0 " for any "c in (0,1)`

C

`f(1//2)gtf(1)`

D

None of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

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

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

    ARIHANT MATHS ENGLISH|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|9 Videos
  • DIFFERENTIATION

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

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuously differentiable function with f'(x)ne0 and satisfies f(0) = 1 and f'(0) = 2 then lim_(xrarr0) (f(x)-1)/(x) is

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

A differentiable function f(x) satisfies f(0)=0 and f(1)=sin1 , then (where f' represents derivative of f)

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these