In today’s class we saw that, given the function \(f(x)=x^2\), we could use a limit to show that the slope of the tangent at any point on that function could be calculated using \(2x\). This new function is called the derivative of \(f\), and \(f'(x)\) is typically used to represent that new function.
So, if \(f(x)=x^2\), we have shown that \(f'(x)=2x\).
Read Section E on pages 355–357, paying particular attention to the examples (which essentially follow the method we used in class).
Complete questions 1, 2, 5cd and 6 on page 357.