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Let $h$ be a twice continuously differentiable positive function on an open interval $J.$ Let $g(x) = ln\left( {h(x)} \right)$ for each $x \in J$. Suppose ${\left( {h'(x)} \right)^2} > h''(x) h(x) $ for each $x \in J$. Then

• A
  $g$ is increasing on $J$
• B
  $g$ is decreasing on $J$
• C
  $g$ is concave up on $J$
• ✓
  $g$ is concave down on $J$