Methods2024 NHT Exam 2 Section A · Q20CAS active1 mark

Translated quartic with absolute maximum at an endpoint

Let $f: R \to R, f(x) = x^2(1 - x^2)$ and $g: [0, 1] \to R, g(x) = f(x - a)$ .

Find all real values of $a$ , such that $g(0)$ is the absolute maximum value of $g$ .

1 mark

a = \pm\frac{\sqrt{2}}{2}

a \in \left[-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right]

a \in \left(-\infty, -\frac{\sqrt{2}}{2}\right] \cup \left[\frac{\sqrt{2}}{2}, \infty\right)

a \in \left[-\frac{\sqrt{2}}{2}, -\frac{1}{2}\right] \cup \left[\frac{1}{2}, \frac{\sqrt{2}}{2}\right]

a \in \left(-\infty, -\frac{\sqrt{2}}{2}\right] \cup \left[\frac{1}{2}, \frac{\sqrt{2}}{2}\right]

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