Identify the function's local and absolute extreme values, if any, saying where they occur.
-$$h ( x ) = \frac { x - 1 } { x ^ { 2 } + 5 x + 10 }$$
A) local minimum at x = -3; no local maxima
B) local minimum at x = -4; local maximum at x = 5
C) local minimum at x = -3; local maximum at x = 5
D) no local extrema

Question

Quizplus · Accepted Answer

The derivative is $$h'(x) = \frac { ( x ^ { 2 } + 5 x + 10 ) - ( x - 1 ) ( 2 x + 5 ) } { ( x ^ { 2 } + 5 x + 10 ) ^ { 2 } } = \frac { 10 } { ( x ^ { 2 } + 5 x + 10 ) ^ { 2 } } > 0$$for all x, so the function is increasing on its entire domain. Therefore, there are no local extrema.

Identify the Function's Local and Absolute Extreme Values, If Any h(x)=x−1x2+5x+10h ( x ) = \frac { x - 1 } { x ^ { 2 } + 5 x + 10 }h(x)=x2+5x+10x−1​

Identify the Function's Local and Absolute Extreme Values, If Any $h ( x ) = \frac { x - 1 } { x ^ { 2 } + 5 x + 10 }$