Explain why each of the following statements is false using words, specic counterexam- ples, and/0r graphs. 1. If f is dened on ((1,1)) and f(c) = 0 at some point c 6 (a,b), then f'(c) = 0. f(x)={2x+1 $30 2. If x2 + 2m x > 0, then f'(0) = 2. 3. The tangent line to the graph of f at a point intersects the graph of f at exactly one point. 4. If f'(a:) > g'(x) for all x 6 (a,b), then f(x) > g(x) for all m E (a, b). 5. If f is a function and f2 is differentiable everywhere, then f is differentiable every where