Consider the function p(x)=x6−6x4+9x2+7 defined for all real x.
a. (i) Solve p′(x)=0 to obtain all stationary points of p.
b. (ii) Use the second derivative to classify each stationary point as a local maximum or a local minimum.
c. (iii) How many local maxima and how many local minima does p possess? List the coordinates of each.
d. (iv) Identify the highest local maximum value and the lowest local minimum value of p, together with the point(s) at which they occur.