All the derivatives of g exist at x 0 and g has a critical

Question

Question: All the derivatives of g exist at x = 0 and g has a critical point at x = 0.

(a) Write the nth Taylor polynomial for g at x = 0.

(b) What does the Second Derivative test for local maxima and minima say?

(c) Use the Taylor polynomial to explain why the Second Derivative test works.