What is the extreme f(x)=(5x)/(x^2+16),0<= x<= 12 ?

The extreme f(x)=(5x)/(x^2+16),0<= x<= 12 is Minimum(0,0),Maximum(4, 5/8),Minimum(12, 3/8)

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extreme f(x)=(5x)/(x^2+16),0<= x<= 12

extreme

Minimum (0, 0), Maximum (4, \frac{5}{8}), Minimum (12, \frac{3}{8})

Solution steps

Find the critical points:

x = 0, x = 4, x = 12

Domain of

\frac{5 x}{x ^{2} + 16}, 0 \leq x \leq 12 : 0 \leq x \leq 12

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < 12

Plug the extreme point

x = 0

into

\frac{5 x}{x ^{2} + 16} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 4

into

\frac{5 x}{x ^{2} + 16} \Rightarrow y = \frac{5}{8}

Maximum (4, \frac{5}{8})

Plug the extreme point

x = 12

into

\frac{5 x}{x ^{2} + 16} \Rightarrow y = \frac{3}{8}

Minimum (12, \frac{3}{8})

Minimum (0, 0), Maximum (4, \frac{5}{8}), Minimum (12, \frac{3}{8})

What is the extreme f(x)=(5x)/(x^2+16),0<= x<= 12 ?
The extreme f(x)=(5x)/(x^2+16),0<= x<= 12 is Minimum(0,0),Maximum(4, 5/8),Minimum(12, 3/8)