Sketching Graphs

[wattsy]

Just wondering if I could get a hand with sketching a graph where you aren't given the function. These are the details that are given -: f(0)=-1 f'(0)=0. f'(2)=0 f'(x) <0 for x <2. f'(x) >0 for 0<x<2. f'(x) <0 for x>2. Any help with finding points would be appreciated

cheers

 

[stapel]

...sketching a graph where you aren't given the function. These are the details that are given:

f(0)=-1 f'(0)=0. f'(2)=0 f'(x) <0 for x <2. f'(x) >0 for 0<x<2. f'(x) <0 for x>2

First, note that there are infinitely-many "correct" answers. This information is sufficient only to allow you to use your knowledge, experience, and imagination in order to create an answer. It is entirely possible that your answer will be an exact match to nobody else in your class.

Use the information to start roughing things in. You'll be making many changes as you go along. Start with the listed point at (x, y) = (0, -1).

You are given that the slope at x = 0 and at x = 2 is zero. What does this tell you about the shape of the graph at these x-values? You are given that the slope is positive between x = 0 and x = 2. What does this tell you about the general shape (increasing or decreasing) of the graph between these two x-values? You are given that the slope is negative to the right of x = 2. What does this tell you?

Note: The "f'(x) < 0 for x < 2" must be a typo, since this contradicts "f'(x) > 0 for 0 < x < 2".