Finding r from r' Find the function r that satisfies the given condition. r'(t) = ⟨et, 2e2t, 6e3t⟩; r(0) = ⟨1, 3, -1⟩

how do i find f(g(x)) and it's domain ? step by step please.

Q4 A function y = f(t) is defined and continuous for all real numbers t on the closed interval [-2.5, 6.5]. The first derivative, y'= f'(t) is sketched below. For each question, give a short and brief explanation. -2 -1 2 -1+ -2+ y 1 2 3 f'(t) 4 (a) At what value(s) of t does the function f has critical point(s)? (b) On what open interval(s), the function f is decreasing. (c) At what t value(s) does the function f has local minimum point(s)? (d) On what open interval does the graph of f concave down on? (e) At what t values does the graph of f has inflection point(s)? 5 6

help on c,d, and e ?