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Let f : [a, b] rarr R be differentiable ...

Let `f : [a, b] rarr R` be differentiable on [a, b] & `k in R`. Let `f(a)= 0 f(b)`. Also let `J(x)= f'(x) -k f(x)`. Then

A

`J(x) gt 0` for all `x in [a, b]`

B

`J(x) lt 0` for all `x in [a, b]`

C

J(x)= 0 has at least one root in (a,b)

D

J(x)= 0 through (a,b)

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