What is the extreme f(x)=xln(x)-2x,1<= x<= 4 ?

The extreme f(x)=xln(x)-2x,1<= x<= 4 is Maximum(1,-2),Minimum(e,-e),Maximum(4,8ln(2)-8)

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extreme f(x)=xln(x)-2x,1<= x<= 4

extreme points

f (x) = x ln (x) - 2 x, 1 \leq x \leq 4

Maximum (1, - 2), Minimum (e, - e), Maximum (4, 8 ln (2) - 8)

Solution steps

Find the critical points:

x = 1, x = e, x = 4

Domain of

x ln (x) - 2 x, 1 \leq x \leq 4 : 1 \leq x \leq 4

Find intervals:

Decreasing

: 1 < x < e,

Increasing

: e < x < 4

Plug the extreme point

x = 1

into

x ln (x) - 2 x \Rightarrow y = - 2

Maximum (1, - 2)

Plug the extreme point

x = e

into

x ln (x) - 2 x \Rightarrow y = - e

Minimum (e, - e)

Plug the extreme point

x = 4

into

x ln (x) - 2 x \Rightarrow y = 8 ln (2) - 8

Maximum (4, 8 ln (2) - 8)

Maximum (1, - 2), Minimum (e, - e), Maximum (4, 8 ln (2) - 8)

f (x) = - 2 x^{2} - 1, - 4 \leq x \leq 3

f (x) = \frac{x}{ln ( 2 x )}

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

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

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

What is the extreme f(x)=xln(x)-2x,1<= x<= 4 ?
The extreme f(x)=xln(x)-2x,1<= x<= 4 is Maximum(1,-2),Minimum(e,-e),Maximum(4,8ln(2)-8)