Task 4: Gradient function of natural log
Explore the gradient function of natural log () by considering the connection between the exponential function and the natural log function. The graphs displayed are , , and . In addition, point P on and point Q on are shown. Tangents are shown at these points and the gradients of the tangents are displayed.
1. What transformation maps the graph to the graph ? Adjust the point P using the slider for p. 2. At any point on the graph, if the gradient of y=e^x is m, what is the gradient of y=ln(x)? (Hint: think about the dimensions of the triangles.) 3. Work out the gradient function for . (At the point , the gradient of is . So at the point , the gradient of is ... So at the point , the gradient of is ...