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1- let f and g be differenciable fn on R and suppose f(0) = g(o) and f dash (x) less than equals to g dash x for all x grter equals o then how we show this gx is grter equal to fx for all x grter equal 0

1- let f and g be differenciable fn on R and suppose f(0) = g(o) and f dash (x) less than equals to g dash x for all x grter equals o then how we show this gx is grter equal to fx for all x grter equal 0

Grade:12

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
f'(x)<=g'(x) for x>0

inegerate (f'(x)-g(x)'<0) between 0 to y
f(y)-g(y)-(f(0)-g(0))= f(y)-g(y)< 0 for all y>0
from above
f(y)< g(y) for all y >0 , replace y by x
f(x)<g(x) for all x>0

sher mohammad
b.tech, iit delhi

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