3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the maximum and minimum values attained by f on the interval [—1, 1].

Suppose f is a differentiable function on an interval II and f(x) 6= 0 for every x in the interval. Prove that f(x) and xf(x) are linearly independent on II.

(4) Let f(x): = ex +1 Using Taylor's Theorem, give real numbers ao, a1, a2, C such that |ƒ(x) − (ao + a₁x + a2x²)| ≤ Cx³.

Find the absolute maximum value of the function f(z) 2² - 40- 2 on the interval-3, 3 . a) O-2 b) 6 c) O 5 d) O3 e) O 2