What is the extreme f(x)=x+(16)/x ,0.2<= x<= 16 ?

The extreme f(x)=x+(16)/x ,0.2<= x<= 16 is Maximum(0.2,80.2),Minimum(4,8),Maximum(16,17)

Popular >

extreme f(x)=x+(16)/x ,0.2<= x<= 16

extreme points

f (x) = x + \frac{16}{x}, 0.2 \leq x \leq 16

Maximum (0.2, 80.2), Minimum (4, 8), Maximum (16, 17)

Solution steps

Find the critical points:

x = 0.2, x = 4, x = 16

Domain of

x + \frac{16}{x}, 0.2 \leq x \leq 16 : 0.2 \leq x \leq 16

Find intervals:

Decreasing

: 0.2 < x < 4,

Increasing

: 4 < x < 16

Plug the extreme point

x = 0.2

into

x + \frac{16}{x} \Rightarrow y = 80.2

Maximum (0.2, 80.2)

Plug the extreme point

x = 4

into

x + \frac{16}{x} \Rightarrow y = 8

Minimum (4, 8)

Plug the extreme point

x = 16

into

x + \frac{16}{x} \Rightarrow y = 17

Maximum (16, 17)

Maximum (0.2, 80.2), Minimum (4, 8), Maximum (16, 17)

f (x) = 3 x^{\frac{5}{3}} - 2 x^{\frac{2}{3}}

g (x) = - x^{3} + 3 x - 10

f (x) = \frac{1}{20} x^{2} - 25 x

f (x) = 3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1

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

What is the extreme f(x)=x+(16)/x ,0.2<= x<= 16 ?
The extreme f(x)=x+(16)/x ,0.2<= x<= 16 is Maximum(0.2,80.2),Minimum(4,8),Maximum(16,17)