1. Use the graph of f(x) = (x+[x|)2 +3 to determine if f'(0) exists. Include an accurate sketch, one in standard window and one where you zoom in. 2. In each case, sketch the graph f (x) , use the graph of f (x) to sketch a graph of f '(x) . Label all important features of f '(x) and f (x) . Hint: Each function has some hidden features that you might not see on the standard window. Be careful. State clearly where f '(x) is not differentiable. A. f(x)=3x%x B. f(x)=3x%(2+x) c. f(x)=28+|13x|+|5x| 3. The acceleration due to gravity, g , is a function of the distance from the center of the Earth, r. Let R be the radius of the Earth, M be the mass of the Earth, and G be the gravitational constant. GMr R3 r 0' (Use denition and make a table) (6 : {mam as 0 m9 + b 0 > 0 Reviewing derivative at a m, by graphs, denition and creating a table of value. 5. For each of the following continuous functions: a) Sketch the graph f (x) , (i) window x:[-1,l] and y:[-2,2], and (ii) window very close to 0 (zoom in at least 3 times near zero.) b) Write f '(0) using the denition (you do not have to evaluate the limit). c) Make a table of values off '(0) to determine if f '(0) exists in each case. If it exist then state f '(0) = , if it does not exist then state f '(O) =DNE (your table should support this answer.) 1 1] x0 A. f(x)= x sin[;] x0 B. f(x)= xsin(x 0 x=0 0 x=0