a. Show that the definition of the derivative applied to the function b. Use a ca...

a. Show that the definition of the derivative applied to the function

b. Use a calculator to evaluate the difference quotient for the following values of h: 0.1, 0.001, and 0.00001. [Hint: Enter the calculation into your calculator with h replaced by 0.1, and then change the value of h by inserting zeros.]

c. From your answers to part (b), does the limit exist? Does the derivative of at x = 0 exist?

d. Graph on the window [-1, 1] by [-1, 1]. Do you see why the slope at x 5 0 does not exist?