What is the extreme f(x)=f(x)=x+(25)/x+9,1<= x<= 50 ?

The extreme f(x)=f(x)=x+(25)/x+9,1<= x<= 50 is Maximum(1,35),Minimum(5,19),Maximum(50, 119/2)

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extreme f(x)=f(x)=x+(25)/x+9,1<= x<= 50

extreme points

f (x) = f (x) = x + \frac{25}{x} + 9, 1 \leq x \leq 50

Maximum (1, 35), Minimum (5, 19), Maximum (50, \frac{119}{2})

Solution steps

Find the critical points:

x = 1, x = 5, x = 50

Domain of

x + \frac{25}{x} + 9, 1 \leq x \leq 50 : 1 \leq x \leq 50

Find intervals:

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < 50

Plug the extreme point

x = 1

into

x + \frac{25}{x} + 9 \Rightarrow y = 35

Maximum (1, 35)

Plug the extreme point

x = 5

into

x + \frac{25}{x} + 9 \Rightarrow y = 19

Minimum (5, 19)

Plug the extreme point

x = 50

into

x + \frac{25}{x} + 9 \Rightarrow y = \frac{119}{2}

Maximum (50, \frac{119}{2})

Maximum (1, 35), Minimum (5, 19), Maximum (50, \frac{119}{2})

f (x, y) = 3 + x^{2} + x y + y^{2}

f (x, y) = x^{2} - 6 x y + 2 y^{2} + 10 x + 2 y - 5

\frac{3}{4} \times \frac{2}{5}

f (x) = 6 x + 7 ln (x)

f (x, y) = - 1 x^{2} - 1 y^{2}

What is the extreme f(x)=f(x)=x+(25)/x+9,1<= x<= 50 ?
The extreme f(x)=f(x)=x+(25)/x+9,1<= x<= 50 is Maximum(1,35),Minimum(5,19),Maximum(50, 119/2)