What is the extreme 3x+7x^{-1} ?

The extreme 3x+7x^{-1} is Maximum(-sqrt(7/3),-2sqrt(21)),Minimum(sqrt(7/3),2sqrt(21))

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extreme 3x+7x^{-1}

extreme points

3 x + 7 x^{- 1}

Maximum (- \frac{7}{3}, - 221), Minimum (\frac{7}{3}, 221)

Solution steps

f^{'} (x) = 3 - \frac{7}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3},

Decreasing

: - \frac{7}{3} < x < 0,

Decreasing

: 0 < x < \frac{7}{3},

Increasing

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

3 x + 7 x^{- 1} : - 221

Maximum (- \frac{7}{3}, - 221)

Plug

x = \frac{7}{3}

into

3 x + 7 x^{- 1} : 221

Minimum (\frac{7}{3}, 221)

Maximum (- \frac{7}{3}, - 221), Minimum (\frac{7}{3}, 221)

\frac{x ^{3} + 1}{x ^{2}}

x^{3} - 9 x^{2} + 24 x

f (x, y) = 2 x^{2} - 4 x + y^{2} - 4 y + 6

p (x) = 2 x^{3} - 11 x^{2} + a x - 40

\frac{x ^{4} - 98 x ^{2}}{8}

What is the extreme 3x+7x^{-1} ?
The extreme 3x+7x^{-1} is Maximum(-sqrt(7/3),-2sqrt(21)),Minimum(sqrt(7/3),2sqrt(21))