Task 2: Gradient of exponential functions
Explore the shape of the gradient function for various exponential functions . The graph of is shown, a point P on the curve is shown with the tangent at that point. The gradient of the tangent is measured, and the value of the gradient is plotted at Q.
Choose a value for a. Press the "trace Q" button. Use the slider to adjust P. 1. What do you notice about the shape of the gradient function of ? Use the slider to set P to be 0. Press "don't trace Q". Use the slider to adjust a. 2. There is an important value of which leads to a special result. Write down the important value of as accurately as you can. Keep a on this important value. Press "Trace Q". Use the slider to adjust P. 3. What do you notice about the gradient function of for this important value of ?