What is the extreme f(x)=16x+9x^{-1} ?

The extreme f(x)=16x+9x^{-1} is Maximum(-3/4 ,-24),Minimum(3/4 ,24)

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extreme f(x)=16x+9x^{-1}

extreme

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

Solution steps

f^{'} (x) = 16 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{4},

Decreasing

: - \frac{3}{4} < x < 0,

Decreasing

: 0 < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < \infty

Plug

x = - \frac{3}{4}

into

16 x + 9 x^{- 1} : - 24

Maximum (- \frac{3}{4}, - 24)

Plug

x = \frac{3}{4}

into

16 x + 9 x^{- 1} : 24

Minimum (\frac{3}{4}, 24)

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

What is the extreme f(x)=16x+9x^{-1} ?
The extreme f(x)=16x+9x^{-1} is Maximum(-3/4 ,-24),Minimum(3/4 ,24)