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# Extrema

How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

A cubic function \(f(x)\) satisfies the following two conditions:

\(A.\) \(f(x)\) has an extreme value \( -4 \) at \( x = 1\ \) and

\(B.\) \(\displaystyle \lim_{x \to 0} \frac{f(x)}{x} = -4 \).

What is the value of \( f(4) \)?

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