Determine if the function is concave up or concave down in the first quadrant.
-$y = x ^ { 3 / 2 }$
A) Concave down
B) Concave up

Question

Quizplus · Accepted Answer

To determine if the function $y = x^{3/2}$ is concave up or concave down, we can examine its second derivative. The first derivative of $y = x^{3/2}$ is $y' = \frac{3}{2}x^{1/2}$, and the second derivative is $y'' = \frac{3}{4}x^{-1/2}$. Since $x^{-1/2}$ is positive for all $x > 0$ (which corresponds to the first quadrant), the second derivative is positive in the first quadrant. A positive second derivative indicates that the function is concave up in the first quadrant.

Determine If the Function Is Concave Up or Concave Down y=x3/2y = x ^ { 3 / 2 }y=x3/2

Determine If the Function Is Concave Up or Concave Down $y = x ^ { 3 / 2 }$