What is the extreme f(x)=x+(49)/x+9,1<= x<= 98 ?

The extreme f(x)=x+(49)/x+9,1<= x<= 98 is Maximum(1,59),Minimum(7,23),Maximum(98, 215/2)

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extreme f(x)=x+(49)/x+9,1<= x<= 98

extreme points

f (x) = x + \frac{49}{x} + 9, 1 \leq x \leq 98

Maximum (1, 59), Minimum (7, 23), Maximum (98, \frac{215}{2})

Solution steps

Find the critical points:

x = 1, x = 7, x = 98

Domain of

x + \frac{49}{x} + 9, 1 \leq x \leq 98 : 1 \leq x \leq 98

Find intervals:

Decreasing

: 1 < x < 7,

Increasing

: 7 < x < 98

Plug the extreme point

x = 1

into

x + \frac{49}{x} + 9 \Rightarrow y = 59

Maximum (1, 59)

Plug the extreme point

x = 7

into

x + \frac{49}{x} + 9 \Rightarrow y = 23

Minimum (7, 23)

Plug the extreme point

x = 98

into

x + \frac{49}{x} + 9 \Rightarrow y = \frac{215}{2}

Maximum (98, \frac{215}{2})

Maximum (1, 59), Minimum (7, 23), Maximum (98, \frac{215}{2})

f (x) = x^{2} + y^{2} - 4 x + 4 y

f (x) = x^{2} + \frac{200}{x}

- 0.1 t^{2} + 0.8 t + 98.8, 0 \leq t \geq 8

x^{8} ln (x)

f (x) = x^{6} + 4 x^{5} + 10

What is the extreme f(x)=x+(49)/x+9,1<= x<= 98 ?
The extreme f(x)=x+(49)/x+9,1<= x<= 98 is Maximum(1,59),Minimum(7,23),Maximum(98, 215/2)