An Exponential Minimum Bound

★ 5/10Extrema calculus Tangent Line Trick

Problem

Let $f(x) = e^x - x$ .

1. Find the equation of the tangent line to $y = f(x)$ at $(0, f(0))$ . 2. Find the extreme values of $f(x)$ . 3. Let $g(x) = f(x) + x^2 + x$ . Prove that the minimum value of $g(x)$ is greater than $\dfrac{1}{2}$ .

Answer

Solution

Difficulty	5/10
Topics	Extrema, calculus, Tangent Line Trick

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