Consider the family of functions defined on the closed interval
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the family of functions gt(x)=(x−t)2 defined on the closed interval [0,4]. Identify the value of x at which gt attains its absolute minimum for each of the three cases: (i) t<0, (ii) 0≤t≤4, and (iii) t>4, and justify your choices in one concise sentence.