MATH 2413 HW 2.2 Due Wednesday, September 16 (1) The graph below is of the function f . Sketch a graph of f . 2.5 -2.4 -1.6 -0.8 0 0.8 1.6 2.4 3.2 4 -2.5 (2) The gure below shows the graph of f, f , and f . Identify each curve and explain your reasons. 1.6 0.8 -1.5 -1 -0.5 0 0.5 1 1.5 2 -0.8 -1.6 (3) (4) (5) (6) Find the derivative of each function below using the limit denition of the derivative. State the domain of the function and the domain of its derivative. f (x) = 2x 5 g(t) = 2 + t 2x h(x) = x1 f (t) = 1 3x (7) f (x) = 2x2 x3 1 2 MATH 2413 HW 2.2 (8) Show carefully using the limit denition that g(x) = |x s| is not dierentiable at s. Find a formula for g (x) and sketch its graph. (9) Let f (x) = x2/3 . Show that f (0) does not exist. Find a counterexample to the following statements. (10) If both functions f (x) and g(x) are dierentiable and f (x) > g(x) on the interval (a, b), then f (x) > g (x) on (a, b). (11) If a function in continuous at a point, then it is dierentiable at that point. (12) If a function is continuous on the interval (a, b) and its graph is a smooth curve (no sharp corners) on that interval, then the function is dierentiable at every point on (a, b). (13) If both functions f (x) and g(x) are not dierentiable at x = a, then f (x) + g(x) is also not dierentiable at x = a