\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f\) be the square root function defined on \([0, +\infty)\) by \(f(x) = \sqrt{x}\).
  1. Justify that \(f\) is strictly concave on \((0, +\infty)\).
  2. Determine the equation of the tangent \(T\) to the graph of \(f\) at the point with abscissa \(1\).
  3. Using the properties of concave functions, prove that for all \(x > 0\), \(\sqrt{x} \le \dfrac{1}{2}(x+1)\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.