What is the extreme f(x)=3x-6/x ,5<= x<= 7 ?

The extreme f(x)=3x-6/x ,5<= x<= 7 is Minimum(5, 69/5),Maximum(7, 141/7)

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extreme f(x)=3x-6/x ,5<= x<= 7

extreme points

f (x) = 3 x - \frac{6}{x}, 5 \leq x \leq 7

Minimum (5, \frac{69}{5}), Maximum (7, \frac{141}{7})

Solution steps

Find the critical points:

x = 5, x = 7

Domain of

3 x - \frac{6}{x}, 5 \leq x \leq 7 : 5 \leq x \leq 7

Find intervals:

Increasing

: 5 < x < 7

Plug the extreme point

x = 5

into

3 x - \frac{6}{x} \Rightarrow y = \frac{69}{5}

Minimum (5, \frac{69}{5})

Plug the extreme point

x = 7

into

3 x - \frac{6}{x} \Rightarrow y = \frac{141}{7}

Maximum (7, \frac{141}{7})

Minimum (5, \frac{69}{5}), Maximum (7, \frac{141}{7})

f (x) = (x^{2} - \frac{7}{3} x + \frac{13}{9}) \cdot e^{3 x}

f (x) = 315 x^{2} + 1260 x^{3}, 0 \leq x \leq 0.25

f (x, y) = 34 - 9 x^{2} - 4 y^{2}

f (x, y) = ln (y^{2} + x) - \frac{1}{2} x + y

What is the extreme f(x)=3x-6/x ,5<= x<= 7 ?
The extreme f(x)=3x-6/x ,5<= x<= 7 is Minimum(5, 69/5),Maximum(7, 141/7)