The second derivative test reveals that f (x) =x²- 5 has A) a relative maximum at $x = \sqrt { 5 }$ B) a point of inflection at $x = \sqrt { 5 }$ C) a relative minimum at x = 0. D) nothing significant at x = 5.

Question

Quizplus · Accepted Answer

The second derivative of $f(x) = x^2 - 5$ is $f''(x) = 2$, which is positive for all $x$. This indicates that the function is concave up everywhere, and thus has a relative minimum at $x = 0$.

The Second Derivative Test Reveals That F (X) =X2- 5 x=5x = \sqrt { 5 }x=5​

The Second Derivative Test Reveals That F (X) =X²- 5 $x = \sqrt { 5 }$