Piecewise Function Optimization Using Second Derivatives – ++ Prep

Piecewise Function Optimization Using Second Derivatives

00:00 4 marks

Consider the function \( f(x) \) defined piecewise on the interval \([-3, 2]\) by:

For \(-3 \leq x < 1\): \( f(x) = -x^2 + 4 \)
For \(1 \leq x \leq 2\): \( f(x) = 2x + 1 \)

Using the second derivative test where applicable and evaluating endpoint values, determine the global maximum value of \( f(x) \) on \([-3, 2]\).

Hint Hint

Hint

Apply the second derivative test on intervals where the function is smooth, and always compare with endpoint values.

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Answer Answer

Complete Answer

The global maximum value is 5, which occurs at \( x = 2 \).

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