Construct the graph of the natural logarithm function from its definition.

• Understand the definition of the natural logarithm function in terms of a definite integral
• Use this definition to relate the value of the natural logarithm function to the area under a curve
• Use the Fundamental Theorem of Calculus to compute the derivative of the natural logarithm function
• Use the derivative of the natural logarithm (1/x) to determine properties of its graph

• natural logarithm function
• area under a curve
• increases without bound
• derivative
• Fundamental Theorem of Calculus

This lesson involves constructing the graph of the natural logarithm function from its definition. As a result, students will:

• Conjecture about the value of the natural logarithm function as x increases without bound.
• Conjecture about the value of the natural logarithm function as x approaches 0 from the right.
• Use the derivative to discover properties of the graph of the natural logarithm function.