f(x) continues in [a,b] interval,and differentiable (a,b) b>a>0

alpha differs 0

proove that there is b>c>a

in that formula:

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my trial:

i mark alpha as "&"

mean theorim says f'(c)=[(f(b)-f(a)]/(b-a)

[f(b)*(a^&) - f(a)*b^&] / [a^& - b^&]= f(c) -c * [(f(b)-f(a)]/[(b-a) * &]

using mean theorem i replaced f'(c)

what should i do next??