What is the extreme f(x)=(32x)/(x^2+16) ?

The extreme f(x)=(32x)/(x^2+16) is Minimum(-4,-4),Maximum(4,4)

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extreme f(x)=(32x)/(x^2+16)

extreme points

f (x) = \frac{32 x}{x ^{2} + 16}

Minimum (- 4, - 4), Maximum (4, 4)

Solution steps

f^{'} (x) = \frac{32 ( - x ^{2} + 16 )}{( x ^{2} + 16 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

\frac{32 x}{x ^{2} + 16} : - 4

Minimum (- 4, - 4)

Plug

x = 4

into

\frac{32 x}{x ^{2} + 16} : 4

Maximum (4, 4)

Minimum (- 4, - 4), Maximum (4, 4)

2 x \cdot e^{- x + 1} + 4

f (x) = 3 x^{3} + y^{3} - 9 x y + 27

f (x) = 15 + 398 x + 184 y - 9 x^{2} - 2 y^{2} - 8 x y

f (x) = cos (x), - \frac{π}{4} \leq x \leq \frac{π}{4}

- 3 x^{2} - 6 x + 3

What is the extreme f(x)=(32x)/(x^2+16) ?
The extreme f(x)=(32x)/(x^2+16) is Minimum(-4,-4),Maximum(4,4)