What is the extreme f(x)=3t+1/t ?

The extreme f(x)=3t+1/t is Maximum(-1/(sqrt(3)),-2sqrt(3)),Minimum(1/(sqrt(3)),2sqrt(3))

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extreme f(x)=3t+1/t

extreme points

f (x) = 3 t + \frac{1}{t}

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

Solution steps

f^{'} (t) = 3 - \frac{1}{t ^{2}}

Find intervals:

Increasing

: - \infty < t < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < t < 0,

Decreasing

: 0 < t < \frac{1}{3},

Increasing

: \frac{1}{3} < t < \infty

Plug

t = - \frac{1}{3}

into

3 t + \frac{1}{t} : - 23

Maximum (- \frac{1}{3}, - 23)

Plug

t = \frac{1}{3}

into

3 t + \frac{1}{t} : 23

Minimum (\frac{1}{3}, 23)

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

f (x) = (x + 1) e^{2 x}

x + 3

y = 24 x^{3} - 3 x^{4} = x^{3} (24 - 3 x)

f (x) = x^{2} + 5 x - 77

f (x) = x^{5} - 5 x^{4} + 5 x^{3} - 10

What is the extreme f(x)=3t+1/t ?
The extreme f(x)=3t+1/t is Maximum(-1/(sqrt(3)),-2sqrt(3)),Minimum(1/(sqrt(3)),2sqrt(3))