Investigating+gradients+of+graphs

=Gradients of Lines and Curves=

You will investigate this task using [|Graph]2 or similar graphing software. Your finished project should be word processed, and ideally presented in a blog that will help you to put together a maths portfolio of work. You should make sure you are communicating your work clearly and explaining WHY things work the way they do.

Plot the graph of y = f(x) where f(x) = x^2. Find the gradient at various points along the graph, and record your findings in a table, something like this:

Can you suggest what the gradient function is?
 * f(x) || -5 || -4 || -3 || -2 || -1 || 0 || 1 || 2 || 3 ||
 * gradient f'(x) || -10 ||  ||   ||   ||   || 0 ||   ||   ||   ||

Try the same thing for y = f(x) + 3, y = f(x) - 2. Can you make a general statement about y = f(x) + c? Why does it work like this?

What about y = 2f(x)? y = 0.5 f(x)? Can you make a general statement for a f(x)? Why does it work like this?

What happens for f(x) = x^3? f(x) =x^4?

If you have found a general rule and described it adequately, try to find gradient functions for some or all of the following:

f(x) = sin x f(x) = cos x f(x) = e^x