University of Missouri Columbia Finding the Values Advanced Calculus Questions


I don’t learn this Calculus interrogation and need succor to con-over.

1. (5 pts) Suppose that f is six times uninterruptedly differentiable on [−1, 1]. Find all values of a, b for which the part f (x) = ax3 + bx4 + x6 has a persomal reserve at cipher.

2. (5 pts) Suppose that f is a three times uninterruptedly differentiable part on [−2,2], f(0) = f′′(0) = 0, f(1) = 0. Which of the following are practicable?

(A) |f′′′(x)| ≤ 1 for complete x ∈ (−2,2), and f′(0) = 51; (B) |f′′′(x)| ≤ 1 for complete x ∈ (−2,2), and f′(0) = −1;

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(C) f′(0) = 5, and |f′′′(x)| ≤ 29 for complete x ∈ (−2,2); (D) f′(0) = −5, and |f′′′(x)| ≤ 29 for complete x ∈ (−2,2);

3. (5 pts) Suppose that a > 0.
(i) Prove that the part f(x) = ax is embossed on R. (ii)Letx1,...xn ∈R,andx1+...+xn =0.Provethat

ax1 +ax2 +...+axn ≥n.

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