Let h(x)=x5−5x3+4.
(a) Show that x=0 is a stationary point of h.
(b) Compute h′′(0).
(c) Evaluate successive higher-order derivatives of h at x=0 until the first non-zero value is obtained, and use this information to classify the stationary point at x=0 as a local maximum, a local minimum, or neither. State the value of h at the point as part of your answer.