Determine two derivatives for the function. Find all the critical points (max/min IP) with the appropriate proof of each. f(x) = x²-7 x+4

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A: The circle passes through three points (3, 8), (9, 6)  and (13, −2).

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A: Upper triangular and orthogonal matrix.

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Q: 1. (i) Consider the transcendental equation f(x) = 2x -x-3. Calculate f(x) for x = -4,-3, -2, -1, 0,…

A: 1.(i) The transcendental equation is                f(x) = 2x - x - 3     Now,            f(-4) =…

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Q: (d) Some tall angry people are friendly.

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Q: 3. Consider the formula A=Vx (p(x) Vq(x)) → (Vx p(x) V Ex q(x)). (a) Show that A is valid. 1 (b)…

A: Given: A=∀x px∨qx→∀x px∨∃x qxTo show: a) A is valid.                b) Converse of A is not valid.

Q: Problem 3 (Ex. 4.16). Suppose that ƒ : A → B and g : B → C are functions. (a) Prove that if g o f is…

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Q: b.) If T € L(V) is self adjoint and UCV is a T-invariant subspace, then U is T-invariant. c.) If T €…

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Q: Find a general solution to the differential equation given below. Primes are derivatives with…

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Q: 6. Suppose N E L(V) is nilpotent and has two Jordan blocks in its Jordan decomposition. Then rank(N)…

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Q: 4. (a) Is the following quantified formula true over the set of integers Z xy(x + y² > 0) Be sure to…

A: Ans-We are given  following quantified formula true over the set of integers Z .