Question

Medal given!!
I need help in the mean value theorem

Answer 1

When I want to apply the mean value theorem \[f \prime (c)=\frac{ f(b)-f(a) }{ b-a}\]
I have to find f(b) and f(a) how can i find them in this question

Answer 2

what are the intervals ? a, b values ?

Answer 3

i know there are no interval in the question

Answer 4

u need to know if a,b >1 or <1 to apply the fun :o

Answer 5

@ikram002p can u explain more ?

Answer 6

if a>=1
then
f(a)=a^2+4
if a<1
f(a)=2a+3

Answer 7

@Abdulhameed i guess the question is to see if f(x) is continuous ?

Answer 8

the question is if mean value theorem can be applied find all the values of c

Answer 9

mean value can definitely be applied, but u must be given some intervals over which to apply MVT. could u post the complete question if possible ? :)

Answer 10

@ganeshie8 the interval is -inf, +inf

Answer 11

i had a similar question this one i took [-1,1] as interval but i couldn't in this one

Answer 12

@AntarAzri i thought of taking -inf,+inf but how can i find f(a)and f(b)

Answer 13

@ganeshie8 i know it can be applied i asked about the interval my problem is in the interval

Answer 14

Mean Value Theorem will apply to any interval where the function is continuous.

Answer 15

@Abdulhameed so you need to see if the function is Continuous, make sure of the Question

Answer 16

@ParthKohli it is continuous on R so i can take any interval on R???

Answer 17

Why not?

Answer 18

it is continuous and differentiable also
and the slope varies from [2, infinity)

interval must be given as input in the problem. you cannot find the interval, atleast it makes no sense to me wat we wud do w/o knowing in which interval to apply MVT :)

Answer 19

depending on the interval chosen u wud get different values for c

Answer 20

all ranging from 2 -> infinity

Answer 21

the question has interval is R but i can't find f(a) and f(b)

Answer 22

can u do me a favor plz ?
take a snapshot and post the original complete question....

Answer 23

@ganeshie8 the question is on a paper and it's handwritten i will type the complete the question

Answer 24

okay ty :))

Answer 25

If mean value theorem can be applied find all values of c in the interval such that \[f \prime(c)=\frac{ f(b)-f(a) }{ b-a } \]

Answer 26

the question have many numbers from 1 to 9 this one is no.6

Answer 27

ohk this is single variable calc version of MVT right ?

Answer 28

what do u mean ?

Answer 29

it has to be finite interval (a, b)
u cannot apply it in R to my knowledge

@experimentX

Answer 30

that what i know too thanks and sorry if i took ur time

Answer 31

np :) wonder how u did the previous questions... u saying there were 8-9 questions like this..

Answer 32

no not like this one they are normal with normal intervals

Answer 33

@ikram002p help

Answer 34

ohk...

Answer 35

there is nothing i can say more than wat u said @ganeshie8
any way the idea of MVT is to find c
such that c between a,b
and f(c) between f(a) and f(b)
so c cud be any number but it depand on finite interval
example