Math  /  Calculus

QuestionFind the intervals where the function f(x)=12x44x2+7 f(x) = \frac{1}{2} x^4 - 4x^2 + 7 is concave upward.

Studdy Solution
Identify the intervals of concavity based on the sign of the second derivative:
The function is concave upward where x>43 x > \sqrt{\frac{4}{3}} or x<43 x < -\sqrt{\frac{4}{3}} .
Thus, the intervals where the function is concave upward are:
(,43)(43,) (-\infty, -\sqrt{\frac{4}{3}}) \cup (\sqrt{\frac{4}{3}}, \infty)
The intervals where the function is concave upward are (,43)(43,) \boxed{(-\infty, -\sqrt{\frac{4}{3}}) \cup (\sqrt{\frac{4}{3}}, \infty)} .

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