Calculus 1 - Lab: Derivatives and Graphs (Chapter 4) Draw a sketch to satisfy each of the given scenarios. 1. The following figure gives the graph of the derivative of a continuous function f that passes through the origin. Sketch a graph of f on the same set of axes. 5 y = f'(x) 2. Sketch the graph of a function f that has a local minimum value where f'(a) = 0. 3. Sketch the graph of a function f that has a local minimum value at x = b where f'(b) is undefined. 4. Sketch the graph of a continuous function f on [ - 2,2] satisfying the given properties. f'(x) =0 for x = - 1 and 0; f has an absolute maximum at x = 2; f has an absolute minimum at x = - 2; and f has a local minimum at x = 0. 5. graph a continuous function f on [0,6] satisfying the given properties. f' is undefined at x = 1 and 4; f'(3) = 0; f has a local maximum at x = 1; f has a local minimum at x = 3; f has an absolute maximum at x = 4; and f has an absolute minimum at x = 6. 6. Sketch the graph of a function that has an absolute maximum, a local minimum, but no absolute minimum on 10.31. 7. Sketch a function that is continuous on ( - co,co) and has the following properties. f'(x) > 0 on ( - co,1); f'(x) 0 on (5,co). 8. Sketch a non-constant function that is continuous on ( - co,co) and has the following properties f(0) = f(4) = f'(0) = f (2) = f'(4) = 0; f(x) 20 on ( - 00,00) 9. Using the following properties of a twice-differentiable 10. Sketch the graph of a function that is continuous on ( - co,co) function y = f(x). select a possible graph of f. and satisfies the following set of conditions. y Derivatives X 0. y" co f'(x)>0 on ( - co,2); f"(x) 0 on (5.7); f'(x) 0 2 -20 y' =0. y">0 x > 2 y' >0, y">0