Seriouly? You post a copy of the problem without any statement at all? You dont say what you understand of the problem or what you have done on the problem.
Did you do what is suggested? This first line says "I want you to pick the version of Newton's Quotient used to calculate derivatives that you feel most comfortable with". Okay, what versions of Newton's Quotient do you know?
I don't know what versions you have seen but I can think of several: \(\displaystyle \frac{f(x+ h)- f(x)}{h}\), \(\displaystyle \frac{f(x+ \Delta x}{\Delta x}\), and \(\displaystyle \frac{f(x_1)- f(x_0)}{x_1- x_0}\).
Do you know any of those? Do you know others? Which do you prefer? Do you see how those are all calculations of the slope of lines, between \(\displaystyle (x+h, f(x+h)\) and \(\displaystyle (x, f(x))\), \(\displaystyle (x+\Delta x, f(x+\Delta x)\) and \(\displaystyle (x, f(x))\), \(\displaystyle (x_1, f(x_1))\) and \(\displaystyle (x_2, f(x_2))\).
Since several points are shown in the picture. Do you see that if you drew the lines from the given blue points through the red point they would be "secants" to the curve? Do you see that the line already drawn through the red point is a "tangent" line? Do you know what a "limit" is? What does a "limit" have to do with the derivative of a function?[/tex][/tex]
