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I need a prove of this result , it a NCERT question .if f(x) is continous in [a,b], and f'(x)>0 in (a,b), Prove that f(x) is increasing in [a,b].( please note the closed nature of the interval ) i feel this is a application of langrange mean value theorem or intermediate theorem. PLease help

MATH SOLVER , 13 Years ago
Grade 12th Pass
anser 2 Answers
Abhay Mishra

Last Activity: 13 Years ago

As f(x) is both continuous and differential...we can apply lagranges theorem

by formula it is sure that for f'(x) to be >0 , b-a should be >0...............

So,a is at lower pt. and b is at higher point..............and hence a increasing function......

 

f'(x)=f'(b)-f'(a)/b-a....

MATH SOLVER

Last Activity: 13 Years ago

You are right b-a>0

but how u reach this point that b is a higher point ( i mean f(b) ) and a is a lower point ,

You are inherently using the result that if f'(x)>0 the function is increasing

hence , b is a higher point and a is a lower point

and how come

f'(x)= (f'(b)-f'(a) )/ (b-a) ???

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