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