Consider the function

a. Use the definition of the derivative to show that f'(0) = 0.
b. Assume the fact that f^(k) (0) = 0, for k = 1, 2, 3, . . . (You can write a proof using the definition of the derivative.) Write the Taylor series for f centered at 0.
c. Explain why the Taylor series for f does not converge to f for x ≠ 0.

Transcribed Image Text:

-1/x² if x + 0 |f(x) if x = 0.