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Die Heuning Pot Literature Guide
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Introduction to Derivatives - At A Glance:

From a graph of a function f(x) we can make a sketched graph of its derivative f ' (x). To do this, we use some things we talked about earlier.

  • If f is decreasing, its slope (and hence its derivative) is negative. If f is increasing, its slope (and hence its derivative) is positive.
      
  • From drawing tangent lines to f, we can compare relative values of the derivative and tell where the derivative is greatest.
      
  • If f is a line, its slope is constant.
      

Be Careful: The word "it" is dangerous.

Look at these two sentences: 

  • It's increasing, so it's positive. 
      
  • f is increasing, so ' is positive.
       

The first sentence is unclear. What does "it" mean? There's no way to know. Whenever we use the words "increasing, decreasing, positive, negative," that we are clear about what (f, f ', or something else?) is increasing, decreasing, positive, or negative.

Example 1

From the graph of f(x), draw a graph of its derivative f'(x).


Example 2

From the graph of f(x), draw a graph of f'(x).


Example 3

From the graph of f(x), draw a graph of f'(x).


Example 4

From the graph of f'(x), draw a graph of f(x).


Example 5

From the graph of f'(x), draw a graph of f(x).


Example 6

From the graph of f'(x), draw a graph of f(x).


Exercise 1

For the function f(x) below, draw a graph of f'(x). Don't worry too much about whether f' is straight or curvy - focus on getting it to cross the x axis in the right places.

Exercise 2

For the function f(x) below, draw a graph of f'(x). Don't worry too much about whether f' is straight or curvy - focus on getting it to cross the x axis in the right places.

Exercise 3

For the function f(x) below, draw a graph of f'(x). Don't worry too much about whether f' is straight or curvy - focus on getting it to cross the x axis in the right places.

Exercise 4

For the function f(x) below, draw a graph of f'(x). Don't worry too much about whether f' is straight or curvy - focus on getting it to cross the x axis in the right places.

Exercise 5

From the graph of f'(x), draw a graph of f(x). Make sure to label each graph.

Exercise 6

From the graph of f'(x), draw a graph of f(x). Make sure to label each graph.

Exercise 7

From the graph of f'(x), draw a graph of f(x). Make sure to label each graph.

Exercise 8

From the graph of f'(x), draw a graph of f(x). Make sure to label each graph.

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