inequality

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

1 practice marks

Original practice question

Given $g(x) = 3x^{\frac{1}{2}} + 2x$ for $x > 0$, find the values of $x$ for which $2 < g'(x) < 5$.

Worked explanation

• Find derivative

  \[g'(x) = \frac{3}{2}x^{-\frac{1}{2}} + 2\]

• Solve the inequality

  \[0 < \frac{3}{2x^{\frac{1}{2}}} < 3 \implies 0 < \frac{1}{\sqrt{x}} < 2 \implies x > \frac{1}{4}\]

$0 < x < \frac{9}{4}$

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