Mr. Sevilla's Math Classroom



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KWL Chart

In this activity, begin by filling out the first two columns. This will give you an idea of what you know about the subject. The last column will be completed at end of Lesson 3.

|Topic: Interpreting Graphs and Functions Using Calculus |

|What I Know |What I Want to Know |What I Learned |

| | | |

|A graph is increasing when the slope |How do I find an absolute maximum and|To find the absolute maximum and minimum we could use the closed |

|of a function is positive. |minimum? |interval method. The closed interval method requires the |

| | |following: |

|A graph is decreasing when the slope | |Finding the critical values of the function (f) and the values of|

|of the function is negative. | |f at the critical values. |

| | |Find the values of f at endpoint [a, b]. |

|A maximum is the highest point on the| |The points from steps a & b the has the largest value of f will |

|graph along the y-axis | |be the absolute maximum and the smallest will be absolute |

| | |minimum. |

|A minimum is the lowest point on the | | |

|graph along the y-axis. | |Critical Values: |

| | |Can be a maximum, minimum or an inflection point. |

|A graph has a slope of zero if it is | |Can be found by taking the first derivative. |

|a straight line along the horizontal |Compare and contrast the difference |Inflection Points: |

|axis. |between the critical values and |The point at which a graph goes from concave up to concave down |

| |inflection points? |or concave down to concave up. |

|The derivative of a function gives us| |Can be found by taking the first and second derivative. |

|the slope of the initial function. | | |

| | |The first derivative allows us to find the critical values and |

| | |some of the inflection points. |

| | | |

| | |The process of the second derivative goes as follows: |

| |What does the first derivative help |Take the derivative of f(x) and set it equal to zero. |

| |us find. |Find the value of f at all critical values and end points. |

| | |Then take the second derivative and substitute the critical |

| |What is the process of the second |values for x into f”(x). |

| |derivative? |If the values from part c are larger than 0 then this is a local |

| | |minimum. |

| | |If the values from part c are smaller than 0 then this is a local|

| | |maximum. |

| | | |

| | |A continuous graph is concave up when the slope of a graph goes |

| | |from decreasing to increasing. Concave up means this will look |

| | |like a happy face. |

| | | |

| | |A continuous graph is concave down when the slope of the graph |

| | |goes from increasing to decreasing. Concave down means this will |

| | |look like a sad face. |

| |Describe the difference between | |

| |concave up and concave down. | |

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