MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let g(x)=∣x−2∣+(x−5)2,x∈R.
(i) Rewrite g as separate algebraic expressions for the intervals x<2 and x≥2.
(ii) For each interval, find g′(x) and hence list all critical points of g.
(iii) Classify every critical point obtained in part (ii) using a suitable test and justify your answer clearly.
(iv) Determine the minimum value of g on the entire real line and the point(s) at which it occurs.