Category: Revolutionary Road Film Questions

I don’t understand this Calculus question and need help to study .
1 . (5 pts) Suppose that f is six times continuously differentiable on
[−1, 1] . Find all values of a, b for which the function f (x) = ax3 + bx4 +
x6 has a local minimum at zero .
2 . (5 pts) Suppose that f is a three times continuously differentiable
function on [−2,2], f(0) = f′′(0) = 0, f(1) = 0 . Which of the following
are possible?
(A) |f′′′(x)| ≤ 1 for every x ∈ (−2,2), and f′(0) = 51;
(B) |f′′′(x)| ≤ 1 for every x ∈ (−2,2), and f′(0) = −1;
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(C) f′(0) = 5, and |f′′′(x)| ≤ 29 for every x ∈ (−2,2);
(D) f′(0) = −5, and |f′′′(x)| ≤ 29 for every x ∈ (−2,2);
3 . (5 pts) Suppose that a > 0 .
(i) Prove that the function f(x) = ax is convex on R .
(ii)Letx1, . . . xn ∈R,andx1+ . . . +xn =0 . Provethat
ax1 +ax2 + . . . +axn ≥n .
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