maximum value

Practise maximum value with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

Let $f: R \to R$, $f(x) = x^2(4 - x^2)$ and $g:[0, 2] \to R$, $g(x) = f(x - a)$. Find all real values of $a$ such that $g(0)$ is the absolute maximum value of $g$.

Worked explanation

• Analyze the function

  \[f(\pm\sqrt{2}) = 2(4-2) = 4\]

• Condition for g(0) to be maximum

  \[a \leq -\sqrt{2} \text{ or } a \geq \sqrt{2} + 2\]

B

Original VectorPaths practice; not an official VCAA question or marking rubric.