What is the extreme f(x)=49x+(16)/x ?

The extreme f(x)=49x+(16)/x is Maximum(-4/7 ,-56),Minimum(4/7 ,56)

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extreme f(x)=49x+(16)/x

extreme points

f (x) = 49 x + \frac{16}{x}

Maximum (- \frac{4}{7}, - 56), Minimum (\frac{4}{7}, 56)

Solution steps

f^{'} (x) = 49 - \frac{16}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{4}{7},

Decreasing

: - \frac{4}{7} < x < 0,

Decreasing

: 0 < x < \frac{4}{7},

Increasing

: \frac{4}{7} < x < \infty

Plug

x = - \frac{4}{7}

into

49 x + \frac{16}{x} : - 56

Maximum (- \frac{4}{7}, - 56)

Plug

x = \frac{4}{7}

into

49 x + \frac{16}{x} : 56

Minimum (\frac{4}{7}, 56)

Maximum (- \frac{4}{7}, - 56), Minimum (\frac{4}{7}, 56)

f (x) = x^{2} + 10 x + 9

f (x) = x - 2, 0 \leq x \leq 4

y = 7 x - 7 z - 9

y, y < 3 x - 4

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

What is the extreme f(x)=49x+(16)/x ?
The extreme f(x)=49x+(16)/x is Maximum(-4/7 ,-56),Minimum(4/7 ,56)