f and g be differentiable on the interva...

f and g be differentiable on the interval I and let `a,b inI, altb`. Then

If `f(a)=0=f(b)`, the equation `f'(x)+f(x)g'(x)=0` is solvable in (a,b).

If `f(a)=0=f(b)`, the equation `f'(x)+f(x)g'(x)=0` may not be solvable in (a,b).

If `g(a)=0=g(b)`, the equation `g'(x)+kg(x)=0` is solvable in (a,b),`kinR`.

If `g(a)=0=g(b)`, the equation `g'(x)+kg(x)=0` may not be solvable in (a,b),`kinR`.

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A, C

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