What is the extreme f(x)=x+(49)/x ,2<= x<= 12 ?

The extreme f(x)=x+(49)/x ,2<= x<= 12 is Maximum(2, 53/2),Minimum(7,14),Maximum(12, 193/12)

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extreme f(x)=x+(49)/x ,2<= x<= 12

extreme points

f (x) = x + \frac{49}{x}, 2 \leq x \leq 12

Maximum (2, \frac{53}{2}), Minimum (7, 14), Maximum (12, \frac{193}{12})

Solution steps

Find the critical points:

x = 2, x = 7, x = 12

Domain of

x + \frac{49}{x}, 2 \leq x \leq 12 : 2 \leq x \leq 12

Find intervals:

Decreasing

: 2 < x < 7,

Increasing

: 7 < x < 12

Plug the extreme point

x = 2

into

x + \frac{49}{x} \Rightarrow y = \frac{53}{2}

Maximum (2, \frac{53}{2})

Plug the extreme point

x = 7

into

x + \frac{49}{x} \Rightarrow y = 14

Minimum (7, 14)

Plug the extreme point

x = 12

into

x + \frac{49}{x} \Rightarrow y = \frac{193}{12}

Maximum (12, \frac{193}{12})

Maximum (2, \frac{53}{2}), Minimum (7, 14), Maximum (12, \frac{193}{12})

f (x) = 3 - 6 x^{2}

f (x, y) = x^{2} + x y - y^{2} - y

f (x) = \frac{( x - 1 ) ^{2}}{x - 3}

f (x) = 3 x^{2} + \frac{48}{x ^{2}}

f (x) = x^{3} - 3 x^{2} - 2 x - 1

What is the extreme f(x)=x+(49)/x ,2<= x<= 12 ?
The extreme f(x)=x+(49)/x ,2<= x<= 12 is Maximum(2, 53/2),Minimum(7,14),Maximum(12, 193/12)