All Common Tangents

★ 6/10functions Extrema calculus Monotonicity Logarithms

Problem

Let $f(x) = x^2 + 2x + 4$ and $g(x) = 2\ln x + 2x + 5$ .

1. Determine the number of zeros of $g(x)$ , with justification. 2. Find the equations of all common tangent lines of the curves $y = f(x)$ and $y = g(x)$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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