Mathematical calculus questions a and b and please explain in detail! Thanks

6. (7 marks) (a) Let f be defined on [3, 45] with f(3) - 50 and f(45) - 2. If f is continuous on the interval (3, 45), is it true that there must be some number ce (3, 45) such that f (c) = 10? If you believe it is true, justify your reasoning. If you believe it is false, show it with an example. I (b) Let g be some function such that g(2) = 1 and lim 9(2 + h) -g(2) -6. Find the value of lim g(a). Please h-+0 h justify all your reasoning