A Boundary Critical Point

★ 7/10functions Extrema calculus Monotonicity Casework

Problem

Let

f(x) = x^2 - 2ax + 4(a-1)\ln(x+1),

where the real number $a < 3$ .

1. Is $x = 1$ a critical (extremum) point of $f(x)$ ? Explain. 2. If $f(x) \leqslant 0$ on the interval $[0, 1]$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Casework

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