TABLE OF CONTENTS

Let f(x) = x^{2}. Find f'(1) using the limit definition of the derivative.

First write down the limit definition to be sure we remember it:

Now fill in our value a = 1 and our function f(x) = x^{2}:

We conclude that f'(1) = 2.

Use the limit definition of the derivative to find f'(1) if

We have a = 1.

Therefore f'(1) = -1.

Use the limit definition of the derivative to find f'(0) if f(x) = |x|.

We have a = 0.

And now we have a problem. If h is positive, the quotient evaluates to 1, so

If h is negative, the quotient evaluates to -1, so

Since the one-sided limits disagree,