Home
Class 12
MATHS
If f (x) is continous on [0,2], differen...

If f (x) is continous on [0,2], differentiable in `(0,2) f (0) =2, f(2)=8 and f '(x) le 3 ` for all x in (0,2), then find the value of f (1).

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
Applying LMVT to f in `[0,1]` and again in `[1,2]` there exist `C_(1)in (0,1)` such that
`(f(1)-f (0))/(1-0) =f'C_(1)1 le 3 impliesf(1) le 5 " "...(i)`
There exist `C _(2) in (1,2),` such that
`(f(2)-f (1))/(2-1) =f'(C_(2))le 3 implies f (1) ge 5`
Hence, (1) and (2) imply that `f (1) =5`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE Main Revision Test-9 | JEE-2020

    VMC MODULES ENGLISH|Exercise SECTION 2|5 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

Similar Questions

Explore conceptually related problems

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .

If f''(x) le0 "for all" x in (a,b) then f'(x)=0

If f(x) is continuous in [0,2] and f(0)=f(2). Then the equation f(x)=f(x+1) has

If f(x) is continuous and differentiable in x in [-7,0] and f'(x) le 2 AA x in [-7,0] , also f(-7)=-3 then range of f(-1)+f(0)

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

If f:R to R is continous such that f(x) -f(x/2)=(4x^(2))/3 for all xinR and f(0)=0, find the value of f(3/2) .

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

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)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