Home
Class 12
MATHS
If f:R to R is a twice differentiable f...

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 :

A

`f'(1) gt 1`

B

`f'(1) le 0`

C

`1/2 lt f'(1) le 1`

D

`0 lt f'(1)= le 1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

if f:R rarr R is a differentiable function such that f'(x)>2f(x) for all x varepsilon R, and f(0)=1, then

If f:R rarr R is a differentiable function such that f(x)>2f(x) for all x in R and f(0)=1, then

Let f:(0,oo)rarr 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:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

If f is twice differentiable function for x in R such that f(2)=5,f'(2)=8 and f'(x) ge 1,f''(x) ge4 , then

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

For all twice differentiable functions f : R to R , with f(0) = f(1) = f'(0) = 0