Cauchy mean value theorem (For f,g continuous on [a,b], differentiable on (a,b) with g'(x)≠0 on)
jee-mainjee-advanced
For f,g continuous on [a,b], differentiable on (a,b) with g'(x)≠0 on (a,b), ∃c: f'(c)/g'(c) = (f(b)−f(a))/(g(b)−g(a))
What each symbol means
| Symbol | What it stands for |
|---|---|
| c | Interior point |
| g | Auxiliary function with nonzero derivative |
When to use this
g(b)≠g(a) typically ensured by g'≠0 on (a,b). f,g continuous [a,b], diff (a,b).