For the following questions let f(x) = 3x².

1. Evaluate the right hand difference quotient for h = 0.01, 0.001 and 0.0001.
2. Use the formal definition of the derivative to find the derivative of f(x) = 3x² at x = 1.
3. Use the nDeriv( command to find the derivative of f(x) = 3x² at x = 1.
4. Find an equation of the line tangent to f(x) = 3x² at x = 1. Graph f(x) = 3x² together with the tangent line and then zoom in to show local linearity.
5. Graph f(x) = 3x² in a [-2, 2, 1] x [-10, 10, 1] window then use the tanimate program with a HIGH sampling rate to illustrate the derivative of f(x) = 3x². Use the program to illustrate the value of the derivative at x = 1.
6. Use linear regression to find the derivative function of f(x) = 3x².

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