Applications of Derivatives
Maxima and Minima
Grade 12
Question:
<p>Let \(A = \text{Minimum}(x^2 - 2x + 7)\), \(x \in \mathbb{R}\) and \(B = \text{Minimum}(x^2 - 2x + 7)\), \(x \in [2, \infty)\). Then:</p>
<p>(a) \(\log_{(B-A)}(A+B)\) is not defined</p>
<p>(b) \(A + B = 13\)</p>
<p>(c) \(\log_{(2B-A)} A < 1\)</p>
<p>(d) \(\log_{(2A-B)} A > 1\)</p>
Step-by-Step Solution
Key Concept: Find the minimum value of the quadratic function on all reals and on the restricted domain, then verify logarithmic properties based on these values
<p>Not provided in source material.</p>
Correct Answer: a, b, c, d