Prove that
(a) every point on the line y = 6 − x is outside the circle with radius 4 and center(−3, 1).
(b) Prove that there exists a three-digit natural number less than 400 with distinct digits, such that the sum of the digits is 17 and the product of the digits is 108.
(c) Use the Extreme Value Theorem to prove that if f does not have a maximum value on the interval [5, 7], then f is not differentiable on [5, 7].
(d) Use Rolle’s Theorem to show that x3 + 6x − 1 = 0 does not have more than one real solution.
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