Question

Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical point of the function f(x, y) = (90)x 2 + (0)xy + (90)y 2 + (−72)x + (96)y + (40), and Q3 = 1 if f has a local minimum at (Q1, Q2), Q3 = 2 if f has a local maximum at (Q1, Q2), Q3 = 3 if f has a saddle point at (Q1, Q2), and Q3 = 4 otherwise. Let Q = ln(3 + |Q1| + 2|Q2| + 3|Q3|). Then T = 5 sin2 (100Q)

satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5

Answer 1

Answer :-

A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but may be) a global minimum.

Relative maximum also called as local maximum. the value of a function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point. Compare absolute maximum.