Determine whether MVT applies to the following functions on the given interval. If so, find the point(s) guaranteed to e

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Determine whether MVT applies to the following functions on the
given interval. If so, find the point(s) guaranteed to exist by
MVT. If the theorem does not apply, clearly explain why.
(a) f(x) = 2x + (x − 1)^1/2 , on [1, 5]
(b) f(x) = x^3/ (1 − √ x) , on [0, 4]
(c) f(x) = (√3 )x + 2 cos x, on [0, 2π]
(d) f(x) = x^2 − x^2/3 , on [−1, 1]