Determine if the function is concave up or concave down in the first quadrant.
-$y = x ^ { 5.4 }$
A) Concave up
B) Concave down

Question

Quizplus · Accepted Answer

To determine if the function $y = x^{5.4}$ is concave up or concave down in the first quadrant, we look at the second derivative of the function. The first derivative is $y' = 5.4x^{4.4}$, and the second derivative is $y'' = 5.4 \times 4.4x^{3.4}$. Since the exponent $3.4$ is positive, $y''$ is positive for all $x > 0$, which corresponds to 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=x5.4y = x ^ { 5.4 }y=x5.4

Determine If the Function Is Concave Up or Concave Down $y = x ^ { 5.4 }$