Copy of Task 3: Gradient function of exponential functions
Explore the algebraic form of the gradient function of exponential functions and meet THE exponential function, .
Adjust the value of a using the slider.
1. What is the general form of the derivative of ?
2. What do you notice about the function/graph and its derivative/gradient for the special value of found in Task 2?
The special value is called "".
3. Use your calculator to find the value of to 3 decimal places.
is an exponential function. is THE exponential function.
Type "f(x)=e^x" into the input box, selecting "e" from the drop-down menu to the right of the box.
4. Write down the derivative of .
5. Hence write down the integral of .