maximum value

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

1 practice marks

Original practice question

Let $f: R \to R$, $f(x) = -x^2 + 4x$ and $g: [0, 3] \to R$, $g(x) = f(x) + k$ where $k$ is a real constant. For which values of $k$ is the maximum value of $g$ equal to $g(2)$?

Worked explanation

• Analyze maximum of g

  \[g(2) = -(2-2)^2 + 4 + k = 4 + k\]

A

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