MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let p(x)=x4−4x3+6x2+1, where x∈R.
(i) Find all critical points of p.
(ii) Determine the intervals of strict increase and strict decrease of p.
(iii) Compute p′′(x) and hence find the intervals where the curve is concave upward and concave downward.
(iv) Using the results of (i)–(iii), sketch an accurate qualitative graph of y=p(x), marking all local maxima, local minima and points of inflection.