I Question 10. III (a) Does there exist afunction g(x) such that g(0) = 1, g(2) : 4, and g'(x) 2 2for all x? (lo) Suppose we have a function f (x) that is continuous on [3, 3] and differentiable on (3, 3). Suppose you are also given f(-3) = 3:f(-2)=1'f(-1)= 0:f(0) = 2;f(1) = 3'f(2) = 4;f(3) = 4 Find an interval of length 2 that is guaranteed to contain a solution for the equation f '(x) = 1. For each part, you must justify your answer properly using Mean Value Theorem. For both questions, note that nothing is known about the values of the function other than the information provided. So we don't have sufficient information to draw the graph of the function, and as such, a picture will not be counted as a proper justification